Journal articles on the topic 'Formal category theory'
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Vickers, P., J. Faith, and N. Rossiter. "Understanding Visualization: A Formal Approach Using Category Theory and Semiotics." IEEE Transactions on Visualization and Computer Graphics 19, no. 6 (June 2013): 1048–61. http://dx.doi.org/10.1109/tvcg.2012.294.
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Fradi, Mouna, Faïda Mhenni, Raoudha Gaha, Abdelfattah Mlika, and Jean-Yves Choley. "Conflict Resolution in Mechatronic Collaborative Design Using Category Theory." Applied Sciences 11, no. 10 (May 14, 2021): 4486. http://dx.doi.org/10.3390/app11104486.
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Due to the multitude of disciplines involved in mechatronic design, heterogeneous languages and expert models are used to describe the system from different domain-specific views. Despite their heterogeneity, these models are highly interrelated. As a consequence, conflicts among expert models are likely to occur. In order to ensure that these models are not contradictory, the necessity to detect and manage conflicts among the models arises. Detecting these inconsistencies at an early stage significantly reduces the amount of engineering activities re-execution. Therefore, to deal with this issue, a formal framework relying upon mathematical concepts is required. The mathematical theory, namely category theory (CT), is considered as an efficient tool to provide a formal and unifying framework supporting conflict detection and management. This paper proposes a comprehensive methodology that allows conflict detection and resolution in the context of mechatronic collaborative design. CT is used in order to explicitly capture the inconsistencies occurred between the disparate expert models. By means of this theory, the conflicts can be detected and handled in an easy and formal way. Our proposed approach is applied to a collaborative scenario concerning the electro-mechanical actuator (EMA) of the aileron.
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Gillibert, Jean, and Christian Retoré. "Category theory, logic and formal linguistics: Some connections, old and new." Journal of Applied Logic 12, no. 1 (March 2014): 1–13. http://dx.doi.org/10.1016/j.jal.2014.01.001.
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Blanc, Anthony, Ludmil Katzarkov, and Pranav Pandit. "Generators in formal deformations of categories." Compositio Mathematica 154, no. 10 (August 30, 2018): 2055–89. http://dx.doi.org/10.1112/s0010437x18007303.
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In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a$k$-linear$\infty$-category for a field$k$. Our main result states that if${\mathcal{C}}$is a$k$-linear$\infty$-category which has a compact generator whose groups of self-extensions vanish for sufficiently high positive degrees, then every formal deformation of${\mathcal{C}}$has zero curvature and moreover admits a compact generator.
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Bénabou, Jean. "Fibered categories and the foundations of naive category theory." Journal of Symbolic Logic 50, no. 1 (March 1985): 10–37. http://dx.doi.org/10.2307/2273784.
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Any attempt to give “foundations”, for category theory or any domain in mathematics, could have two objectives, of course related.(0.1) Noncontradiction: Namely, to provide a formal frame rich enough so that all the actual activity in the domain can be carried out within this frame, and consistent, or at least relatively consistent with a well-established and “safe” theory, e.g. Zermelo-Frankel (ZF).(0.2) Adequacy, in the following, nontechnical sense:(i) The basic notions must be simple enough to make transparent the syntactic structures involved.(ii) The translation between the formal language and the usual language must be, or very quickly become, obvious. This implies in particular that the terminology and notations in the formal system should be identical, or very similar, to the current ones. Although this may seem minor, it is in fact very important.(iii) “Foundations” can only be “foundations of a given domain at a given moment”, therefore the frame should be easily adaptable to extensions or generalizations of the domain, and, even better, in view of (i), it should suggest how to find meaningful generalizations.(iv) Sometimes (ii) and (iii) can be incompatible because the current notations are not adapted to a more general situation. A compromise is then necessary. Usually when the tradition is very strong (ii) is predominant, but this causes some incoherence for the notations in the more general case (e.g. the notation f(x) for the value of a function f at x obliges one, in category theory, to denote the composition of arrows (f, g) → g∘f, and all attempts to change this notation have, so far, failed).
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López, Luis. "On the (Non)complementarity of θ-Theory and Checking Theory." Linguistic Inquiry 32, no. 4 (October 2001): 694–716. http://dx.doi.org/10.1162/002438901753373050.
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Chomsky (1995) proposes that the θ system and the checking system form two complementary modules. As a consequence both subjects and objects must form nontrivial chains to check their formal features with a functional category (T and v, respectively). I argue that objects and exceptional-Case-marking subjects check their formal features with a lexical verb, whose domain is therefore both θ role assigning and feature checking. I showthat discarding the complementarity assumption in this manner results in a more “bare” theory of the computational system as well as several empirical advantages.
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Mabrok, Mohamed A., and Michael J. Ryan. "Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering." Applied Mathematics & Information Sciences 11, no. 1 (January 1, 2017): 43–51. http://dx.doi.org/10.18576/amis/110106.
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Sukharev, A. "The unobservable as an economic category." Obshchestvo i ekonomika, no. 3 (2022): 35. http://dx.doi.org/10.31857/s020736760019060-5.
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The definition of the unobservable in the field of science is given. The ideas about the unobservable in philosophy, physics, economics, etc. are presented. In economic science, the unobservable is presented in two perspectives: as unobservable objects and processes and as constructed categories (concepts) designed to reflect the essential aspects of economic life. The role of abstractions in economic theory is shown. Economic theory is a collection of unobservable abstractions, and its development takes place on the basis of the construction of new abstractions. The system of abstractions, being a formal system, forms a particular economic theory, and the aggregate of those represents a general economic theory. A hypothesis about the internal non-contradictoriness of private economic theories is stated.
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Li, Hong, and Xiao Ping Ma. "Granular Structure Merging Algorithm Based on Category Theory." Applied Mechanics and Materials 128-129 (October 2011): 390–96. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.390.
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In order to solve the problem of conversion from the finer level of granularity to the coarser level of granularity, this paper proposes a formal method for Granular structure merging based on category theory. Firstly, it takes the granular structure as the granular object and the granular structure mapping as the granular morphism, then the granular object and the granular morphism compose the granular structure category. Secondly, it uses the granular morphism and the granular pushout to achieve the granular structure merging , then gets the granular structure merging algorithm (GrSM). Finally, the author illustrates the method with the concrete examples, which solves the granular structure merging issue. This method has a solid mathematical foundation and methodology, which is worth further study.
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Wang, Yonghao. "Law as an important category in the ancient Chinese formal criticism." Frontiers of Literary Studies in China 4, no. 1 (February 12, 2010): 117–37. http://dx.doi.org/10.1007/s11702-010-0006-1.
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Cordier, Jean-Marc, and Timothy Porter. "Vogt's theorem on categories of homotopy coherent diagrams." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 1 (July 1986): 65–90. http://dx.doi.org/10.1017/s0305004100065877.
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Let Top be the category of compactly generated topological spaces and continuous maps. The category, Top, can be given the structure of a simplicially enriched category (or S-category, S being the category of simplicial sets). For A a small category, Vogt (in [22]) constructed a category, Coh (A, Top), of homotopy coherent A-indexed diagrams in Top and homotopy classes of homotopy coherent maps, and proved a theorem identifying this as being equivalent to Ho (TopA), the category obtained from the category of commutative A-indexed diagrams by localizing with respect to the level homotopy equivalences. Thus one of the important consequences of Vogt's result is that it provides concrete coherent models for the formal composites of maps and formal inverses of level homotopy equivalences which are the maps in Ho (TopA). The usefulness of such models and in general of Vogt's results is shown in the series of notes [14–17] by the second author in which those results are applied to give an obstruction theory applicable in prohomotopy theory.
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Declerck, Renaat. "Two notes on the theory of definiteness." Journal of Linguistics 22, no. 1 (March 1986): 25–39. http://dx.doi.org/10.1017/s0022226700010549.
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The terms definite and indefinite, when used in relation to NPs, can be handled in two different ways. One can treat definiteness as a formal (syntactico-morphological) category and make use of the syntactic features [±definite], as in Chomsky (1965). One can also go into the question of how definite and indefinite NPs are used, i.e. the question of when and why a (formally) definite NP is preferred to an indefinite one, or vice versa. If we take the latter approach, we are investigating definiteness as a semantico-pragmatic category.
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Porst, Hans-E. "The formal theory of hopf algebras Part I: Hopf monoids in a monoidal category." Quaestiones Mathematicae 38, no. 5 (June 11, 2015): 631–82. http://dx.doi.org/10.2989/16073606.2014.981736.
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Diskin, Zinovy, and Tom Maibaum. "Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond." Electronic Proceedings in Theoretical Computer Science 93 (August 21, 2012): 1–21. http://dx.doi.org/10.4204/eptcs.93.1.
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Harnik, Victor, and Michael Makkai. "Lambek's categorical proof theory and Läuchli's abstract realizability." Journal of Symbolic Logic 57, no. 1 (March 1992): 200–230. http://dx.doi.org/10.2307/2275186.
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In this paper we give an introduction to categorical proof theory, and reinterpret, with improvements, Läuchli's work on abstract realizability restricted to propositional logic (but see [M1] for predicate logic). Partly to make some points of a foundational nature, we have included a substantial amount of background material. As a result, the paper is (we hope) readable with a knowledge of just the rudiments of category theory, the notions of category, functor, natural transformation, and the like. We start with an extended introduction giving the background, and stating what we do with a minimum of technicalities.In three publications [L1, 2, 3] published in the years 1968, 1969 and 1972, J. Lambek gave a categorical formulation of the notion of formal proof in deductive systems in certain propositional calculi. The theory is also described in the recent book [LS]. See also [Sz].The basic motivation behind Lambek's theory was to place proof theory in the framework of modern abstract mathematics. The spirit of the latter, at least for the purposes of the present discussion, is to organize mathematical objects into mathematical structures. The specific kind of structure we will be concerned with is category.In Lambek's theory, one starts with an arbitrary theory in any one of several propositional calculi. One has the (formal) proofs (deductions) in the given theory of entailments A ⇒ B, with A and B arbitrary formulas. One introduces an equivalence relation on proofs under which, in particular, equivalent proofs are proofs of the same entailment; equivalence of proofs is intended to capture the idea of the proofs being only inessentially different. One forms a category whose objects are the formulas of the underlying language of the theory, and whose arrows from A to B, with the latter arbitrary formulas, are the equivalence classes of formal proofs of A ⇒ B.
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Pócs, Jozef, and Jana Pócsová. "On Bonds for Generalized One-Sided Concept Lattices." Mathematics 9, no. 3 (January 21, 2021): 211. http://dx.doi.org/10.3390/math9030211.
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The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms.
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Duits, Rufus. "Towards a teleo-semiotic theory of individuation." Semiotica 2016, no. 213 (November 1, 2016): 281–305. http://dx.doi.org/10.1515/sem-2015-0103.
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AbstractThis article attempts to develop a sketch or working model of a semiotic theory of individuation from a formalization of basic teleological structures. After caveats and provisional definitions, a formal apparatus is introduced that schematizes teleological structures by way of mathematical category theory. This is then combined with a commutation test for formal systems. Once the formal construction is sufficient, the extent to which the model can account for the operation by which objects, modes, kinds, and attributes become individuated from the “pure multiplicity” of indeterminate being is analyzed. Subsequently, the model is applied to a series of well-known problems in metaphysics and ontology – persistence, change, vagueness, coincidence, mereology, and universals – in order to demonstrate its effectiveness. The metaphysical picture that results from this application is positioned between the conventional extremes of realism and anti-realism: a semiotic anti-/realism. Empirical evidence is then also marshalled in support of the model by way of invocation and analysis of recent research into the development of the perceptual capacities of infants.
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ČUBRIĆ, DJORDJE, PETER DYBJER, and PHILIP SCOTT. "Normalization and the Yoneda embedding." Mathematical Structures in Computer Science 8, no. 2 (April 1998): 153–92. http://dx.doi.org/10.1017/s0960129597002508.
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We show how to solve the word problem for simply typed λβη-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. The formal setting for these results is [Pscr ]-category theory, a version of ordinary category theory where each hom-set is equipped with a partial equivalence relation. The part of [Pscr ]-category theory we develop here is constructive and thus permits extraction of programs from proofs. It is important to stress that in our method we make no use of traditional proof-theoretic or rewriting techniques. To show the robustness of our method, we give an extended treatment for more general λ-theories in the Appendix.
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Wang, Longchun, Lankun Guo, and Qingguo Li. "Continuous Domains in Formal Concept Analysis*." Fundamenta Informaticae 179, no. 3 (April 15, 2021): 295–319. http://dx.doi.org/10.3233/fi-2021-2025.
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Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.
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Kovalyov, S. P. "Design of Heterogeneous Cyber-Physical Systems Employing Category Theory." Mekhatronika, Avtomatizatsiya, Upravlenie 23, no. 2 (February 6, 2022): 59–67. http://dx.doi.org/10.17587/mau.23.59-67.
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Heterogeneous cyber-physical control systems based on digital twins are in demand by Industry 4.0. In accordance with the contemporary systems engineering methodology, such systems are designed at the level of digital models. The paper proposes approaches to formalization and subsequent automation of solving direct and inverse problems of their design. To unify descriptions of heterogeneous components, we follow a viewpoint-based approach to architecture design recommended by the international standard ISO/IEC/IEEE 42010. Following recent trends, we employ category theory as a mathematical framework for the formal description and solution of design problems. Indeed, category theory is a branch of higher algebra specifically aimed at a unified representation of objects of different nature and relationships between them. The design space of a heterogeneous cyber-physical system is constructed as a subcategory of the multicomma category, the objects of which describe possible system architectures with a fixed structural hierarchy represented from a certain viewpoint as diagrams, and morphisms denote actions associated with the parts selection and replacement during the system design. Direct design problems consist in evaluating the properties of the system as a whole by its architecture and are solved using a universal category-theoretic construction of the colimit of the diagram. The solution of inverse problems that require finding variants of the system architecture, which are (sub-, Pareto-) optimal according to the consumer quality criteria, consists in reconstructing diagrams by their colimit edges. For such reconstruction, optimization algorithms of gradient descent type are reasonable to employ, which navigate along the system design space morphisms calculating the path by means of computer algebra. Typical techniques of assembling cyber-physical systems, such as modular composition and aspect weaving, are described in the language of category theory and illustrated. As an example, we outline the design of energy-efficient robotic production lines represented from the behavior viewpoint as discrete-event simulation models.
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Miyake, Masatake, and Yoshiaki Hashimoto. "Newton polygons and gevrey indices for linear partial differential operators." Nagoya Mathematical Journal 128 (December 1992): 15–47. http://dx.doi.org/10.1017/s0027763000004207.
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This paper is a continuation of Miyake [7] by the first named author. We shall study the unique solvability of an integro-differential equation in the category of formal or convergent power series with Gevrey estimate for the coefficients, and our results give some analogue in partial differential equations to Ramis [10, 11] in ordinary differential equations.In the study of analytic ordinary differential equations, the notion of irregularity was first introduced by Malgrange [3] as a difference of indices of a differential operator in the categories of formal power series and convergent power series. After that, Ramis extended his theory to the category of formal or convergent power series with Gevrey estimate for the coefficients. In these studies, Ramis revealed a significant meaning of a Newton polygon associated with a differential operator.
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Blanton, C. D. "Theory by Analogy." PMLA/Publications of the Modern Language Association of America 130, no. 3 (May 2015): 750–58. http://dx.doi.org/10.1632/pmla.2015.130.3.750.
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A is—A.—G. W. F. Hegel (Science of Logic 415)The thing stated and the restatement have constituted an analogy.—Wallace Stevens (129)M-C-M'.—Karl Marx (257)There is a hint of Minerva's owl in medieval philosophy's relation to the apparently mundane formal question of analogy. The problem is everywhere in scholastic thought, inherited from Aristotle and Averroës, then adapted as one of the basic formal mechanisms through which Thomistic logic both transposes its own theological categories onto an older classical framework and apprehends metaphysical relations of being, of identity and difference. Classically, it is by analogy that one conceives the likeness of the unlike, extracting a concept from the individual instances and scattered genera in which it otherwise resides: the quality of wisdom that characterizes God, say, but might differently characterize humans; the property of animation that attaches to humans but differently qualifies beasts. Hegel notes this problem of scholastic analogy in his Lectures on the History of Philosophy, when he comments of Aquinas that the category of “substance (forma substantialis) is, for instance, analogous to” Aristotle's notion of entelechy (3: 71) or when he dismisses medieval Latin more generally as “a quite unsuitable instrument” for the consideration of older philosophical forms—in effect, an imprecise exercise in analogy (38).
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Basti, Gianfranco. "The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic." Philosophies 7, no. 6 (October 26, 2022): 121. http://dx.doi.org/10.3390/philosophies7060121.
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This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences.
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Dai, Shouxin, and Marc Levine. "Connective Algebraic K-theory." Journal of K-Theory 13, no. 1 (January 2, 2014): 9–56. http://dx.doi.org/10.1017/is013012007jkt249.
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AbstractWe examine the theory of connective algebraic K-theory, , defined by taking the −1 connective cover of algebraic K-theory with respect to Voevodsky's slice tower in the motivic stable homotopy category. We extend to a bi-graded oriented duality theory when the base scheme is the spectrum of a field k of characteristic zero. The homology theory may be viewed as connective algebraic G-theory. We identify for X a finite type k-scheme with the image of in , where is the abelian category of coherent sheaves on X with support in dimension at most n; this agrees with the (2n,n) part of the theory of connective algebraic K-theory defined by Cai. We also show that the classifying map from algebraic cobordism identifies with the universal oriented Borel-Moore homology theory having formal group law u + υ − βuυ with coefficient ring ℤ[β]. As an application, we show that every pure dimension d finite type k-scheme has a well-defined fundamental class [X]CK in ΩdCK(X), and this fundamental class is functorial with respect to pull-back for l.c.i. morphisms.
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PAINE, JOSHUA. "Kelsen, Legal Normativity, and Formal Justice in International Relations." Leiden Journal of International Law 26, no. 4 (November 8, 2013): 1037–53. http://dx.doi.org/10.1017/s092215651300054x.
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Hans Kelsen's vast body of work is perhaps one of the best examples of the unremarkable but important point that one's legal theory and methodological choices are intricately tied up with how one understands international law. Kelsen stands for a huge number of different positions, but chief amongst them must be his insistence on developing a ‘pure’ theory of law that accounted for the unique normativity of law, separate from empirical facts and causality on the one hand, and substantive theories of justice on the other. For Kelsen, the unique normativity of law is found within the legal system itself, in the idea of normative imputation – the ‘linking of a conditioning material fact with a conditioned consequence’. According to Kelsen, this specifically legal sense of ‘ought’ is an a priori category that allows us to correctly cognize the legal meaning of empirical data.
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Solomon, Jake P., and Misha Verbitsky. "Locality in the Fukaya category of a hyperkähler manifold." Compositio Mathematica 155, no. 10 (September 6, 2019): 1924–58. http://dx.doi.org/10.1112/s0010437x1900753x.
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Let $(M,I,J,K,g)$ be a hyperkähler manifold. Then the complex manifold $(M,I)$ is holomorphic symplectic. We prove that for all real $x,y$, with $x^{2}+y^{2}=1$ except countably many, any finite-energy $(xJ+yK)$-holomorphic curve with boundary in a collection of $I$-holomorphic Lagrangians must be constant. By an argument based on the Łojasiewicz inequality, this result holds no matter how the Lagrangians intersect each other. It follows that one can choose perturbations such that the holomorphic polygons of the associated Fukaya category lie in an arbitrarily small neighborhood of the Lagrangians. That is, the Fukaya category is local. We show that holomorphic Lagrangians are tautologically unobstructed. Moreover, the Fukaya $A_{\infty }$ algebra of a holomorphic Lagrangian is formal. Our result also explains why the special Lagrangian condition holds without instanton corrections for holomorphic Lagrangians.
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ROBERTS, JOHN E., GIUSEPPE RUZZI, and EZIO VASSELLI. "NET BUNDLES OVER POSETS AND K-THEORY." International Journal of Mathematics 24, no. 01 (January 2013): 1350001. http://dx.doi.org/10.1142/s0129167x13500018.
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We continue studying net bundles over partially ordered sets (posets), defined as the analogues of ordinary fiber bundles. To this end, we analyze the connection between homotopy, net homology and net cohomology of a poset, giving versions of classical Hurewicz theorems. Focusing our attention on Hilbert net bundles, we define the K-theory of a poset and introduce functions over the homotopy groupoid satisfying the same formal properties as Chern classes. As when the given poset is a base for the topology of a space, our results apply to the category of locally constant bundles.
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Lathifah, Syifa'ul, and Januarius Mujiyanto. "Formal Shifts Use on Achieving Pragmatic Equivalence in English – Indonesian Translation of KungFu Panda." English Education Journal 11, no. 4 (December 23, 2021): 465–72. http://dx.doi.org/10.15294/eej.v11i1.45412.
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This study is concerned with the analysis of Catford’s formal shifts use in speech act translation from English into Bahasa Indonesia in Kung Fu Panda movie. The analysis covers the use of level shift and category shift on achieving pragmatic equivalence and how the visual-verbal relation happened along with the pragmatic achievement process. This study took documentation and a questionnaire on collecting the data. In this study, a theory from Baker (1992) was applied to analyze pragmatic equivalence achievement. Moreover, the theory from Halliday (1994) in Martinec and Salway (2005) was used to identify visual-verbal relations. The results of the study depicted (1) the use of level shift and category shift were very needed which led to pragmatic equivalence achievement (95,3%). Based on the target readers and expert raters, (2) the visual-verbal relation helped the translator on target text arrangement by providing the context of which the speech act was being uttered. The visual-verbal relation identified in the Kung Fu Panda movie were exposition (12,7%), enhancement (9,3%), extension (5,3%) and locution relation (72,7%). (3) The translator tended to use category shift dominantly (66,67%) for recreating the most suitable target text that was similar to the source text’s pragmatic meaning.The large identification of visual-verbal relation locutionallowed target and expert readers to perceive the meaning lied in speech act only from the word given.
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Kirkpatrick, Graeme. "Formal Bias and Normative Critique of Technology Design." Techné: Research in Philosophy and Technology 17, no. 1 (2013): 25–46. http://dx.doi.org/10.5840/techne20131713.
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Andrew Feenberg’s distinction between formal and substantive bias in the design of technology is interrogated. The two dimensions of his definition—intention and the enhancement of specific social interests—are examined and eight logical possibilities arising from his argument are identified. These possibilities are explored through discussion of examples and it is argued that Feenberg has both: a) not broken sufficiently with substantivist philosophies of technology so that he retains ambivalence on technology’s ‘biased essence,’ and b) illegitimately rejected the idea of a technology that is biased in itself. The latter category is important to critical theory of technology and the paper offers a conceptualization of it that draws on Habermas’s discourse ethics.
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Perháč, Ján, Valerie Novitzká, William Steingartner, and Zuzana Bilanová. "Formal Model of IDS Based on BDI Logic." Mathematics 9, no. 18 (September 17, 2021): 2290. http://dx.doi.org/10.3390/math9182290.
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Computer network security is an important aspect of computer science. Many researchers are trying to increase security using different methods, technologies, or tools. One of the most common practices is the deployment of an Intrusion Detection System (IDS). The current state of IDS brings only passive protection from network intrusions, i.e., IDS can only detect possible intrusions. Due to that, the manual intervention of an administrator is needed. In our paper, we present a logical model of an active IDS based on category theory, coalgebras, linear logic, and Belief–Desire–Intention (BDI) logic. Such an IDS can not only detect intrusions but also autonomously react to them according to a defined security policy. We demonstrate our approach on a motivating example with real network intrusions.
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Cafezeiro, Isabel, José Viterbo, Alexandre Rademaker, Edward Hermann Haeusler, and Markus Endler. "Specifying ubiquitous systems through the algebra of contextualized ontologies." Knowledge Engineering Review 29, no. 2 (March 2014): 171–85. http://dx.doi.org/10.1017/s0269888914000046.
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AbstractIn order to be able to specify and design ubiquitous applications, it is necessary to rely on a precise and formal representation of context. Aiming at reducing the gap between the formal specification and the design of a concrete ubiquitous application, we have proposed an approach to specify a context-aware system at three levels of abstraction. This specification uses the Algebra of Contextualized Ontologies, which is based on Category Theory and takes contextualization as a basic notion, proposing a small set of simple and powerful operations to compose and decompose contextualized ontologies. In this paper, we present a revised version of the algebra and algorithms to compute the algebraic operations. We exemplify our approach along with a concrete ubiquitous computing scenario. Moreover, by taking advantage of Category Theory foundations, we show that it is possible to derive the algorithms for each algebraic operation from simple modifications of a single basic algorithm.
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Vidalie, Julien, Michel Batteux, Faïda Mhenni, and Jean-Yves Choley. "Category Theory Framework for System Engineering and Safety Assessment Model Synchronization Methodologies." Applied Sciences 12, no. 12 (June 9, 2022): 5880. http://dx.doi.org/10.3390/app12125880.
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In recent decades, there has been a significant increase in systems’ complexity, leading to a rise in the need for more and more models. Models created with different intents are written using different formalisms and give diverse system representations. This work focuses on the system engineering domain and its models. It is crucial to assert a critical system’s compliance with its requirements. Thus, multiple models dedicated to these assertions are designed, such as safety or multi-physics models. As those models are independent of the architecture model, we need to provide means to assert and maintain consistency between them if we want the analyses to be relevant. The model synchronization methodologies give means to work on the consistency between the models through steps of abstraction to a common formalism, comparison, and concretization of the comparison results in the original models. This paper proposes a mathematical framework that allows for a formal definition of such a consistency relation and a mathematical description of the models. We use the context of category theory, as this is a mathematical theory providing great tools for taking into account different abstraction levels and composition of relations. Finally, we show how this mathematical framework can be applied to a specific synchronization methodology with a realistic study case.
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Angiuli, Carlo, Guillaume Brunerie, Thierry Coquand, Robert Harper, Kuen-Bang Hou (Favonia), and Daniel R. Licata. "Syntax and models of Cartesian cubical type theory." Mathematical Structures in Computer Science 31, no. 4 (April 2021): 424–68. http://dx.doi.org/10.1017/s0960129521000347.
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AbstractWe present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, suspension, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgmental equality rules defining the Kan operation on each type. The Kan operation uses both a different set of generating trivial cofibrations and a different set of generating cofibrations than the Cohen, Coquand, Huber, and Mörtberg (CCHM) model. Next, we describe a constructive model of this type theory in Cartesian cubical sets. We give a mechanized proof, using Agda as the internal language of cubical sets in the style introduced by Orton and Pitts, that glue, Π, Σ, path, identity, boolean, natural number, suspension types, and the universe itself are Kan in this model, and that the universe is univalent. An advantage of this formal approach is that our construction can also be interpreted in a range of other models, including cubical sets on the connections cube category and the De Morgan cube category, as used in the CCHM model, and bicubical sets, as used in directed type theory.
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Lekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for higher-dimensional pairs of pants." Compositio Mathematica 156, no. 7 (June 18, 2020): 1310–47. http://dx.doi.org/10.1112/s0010437x20007150.
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Using Auroux’s description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^{n}$, for $k\geqslant n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $n+2$ generic hyperplanes in $\mathbb{C}P^{n}$ ($n$-dimensional pair of pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolution of the derived category of the singular affine variety $x_{1}x_{2}\ldots x_{n+1}=0$. By localizing, we deduce that the (fully) wrapped Fukaya category of the $n$-dimensional pair of pants is equivalent to the derived category of $x_{1}x_{2}\ldots x_{n+1}=0$. We also prove similar equivalences for finite abelian covers of the $n$-dimensional pair of pants.
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Andrason, Alexander, and Michael Karani. "Conative calls to animals: From Arusa Maasai to a cross-linguistic prototype." Lodz Papers in Pragmatics 17, no. 1-2 (July 1, 2021): 3–41. http://dx.doi.org/10.1515/lpp-2021-0002.
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Abstracct The present article expands our empirical and theoretical knowledge of conative animal calls (CACs) in the languages of the world. By drawing on canonical typology and prototype theory – and by contrasting the original evidence related to the category of CACs in Arusa Maasai with the evidence concerning CACs in other languages that is currently available in scholarship – the authors design a cross-linguistic prototype of a CAC and enumerate its 18 prototypical non-formal (semantic-pragmatic) and formal (phonetic, morphological, and syntactic) features.
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Spencer, John P., Vanessa R. Simmering, and Anne R. Schutte. "Toward a formal theory of flexible spatial behavior: Geometric category biases generalize across pointing and verbal response types." Journal of Experimental Psychology: Human Perception and Performance 32, no. 2 (2006): 473–90. http://dx.doi.org/10.1037/0096-1523.32.2.473.
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Thiry, Laurent, and Michel Hassenforder. "A Calculus for (Meta)Models and Transformations." International Journal of Software Engineering and Knowledge Engineering 24, no. 05 (June 2014): 715–30. http://dx.doi.org/10.1142/s0218194014500272.
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This paper proposes a formal representation of modeling languages based on category theory. These languages are generally described by "metamodels", i.e. structures composed by classes and relations, and related by "transformations". Thus, this paper studies how the key categorical concepts such as functors and relations between functors (called natural transformations) can be used for equational reasoning about modeling artifacts (models, metamodels, transformations). As a result, this paper proposes a formal point of view of models usable to specify/prove equivalence between models or transformations (with an application to refactoring).
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Ma, Zizhu. "Generalized Enrichments of Categories for Operads." Algebra Colloquium 14, no. 01 (March 2007): 61–78. http://dx.doi.org/10.1142/s1005386707000077.
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Most enriched categories also have an ordinary category structure which is compatible with the enrichment on them. In this paper, enrichments in a monoidal category are generalized to arbitrary categories. These specialize to the classical enrichments when sets are regraded as discrete categories. We also generalize the definitions of PROs and PROPs as some generalized enrichments of categories. Then an operad in some monoidal category corresponds to a generalized PROP. Algebras of operads induce some special kind of monoidal functors. In the category of small categories, we construct several operads to define lax monoids and lax commutative monoids which are formal descriptions of natural associativity and commutativity. Using this identification, operads and their algebras can be studied by lax commutative monoids and morphisms between them.
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Mello, John Edmund, Ila Manuj, and Daniel John Flint. "Leveraging grounded theory in supply chain research: A researcher and reviewer guide." International Journal of Physical Distribution & Logistics Management 51, no. 10 (September 28, 2021): 1108–29. http://dx.doi.org/10.1108/ijpdlm-12-2020-0439.
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PurposeThe purpose of this article is to identify and explain most frequently misunderstood steps in the use of grounded theory (GT) as a methodology and provide guidance on proper execution of these elements.Design/methodology/approachThis research provides meaningful guidance to both reviewers and authors interested in applying GT. This research is expected to advance the pursuit of formal theory development.FindingsThere are four most frequently misunderstood steps in the use of GT as a methodology. These are related to the use of literature, theoretical sampling, core category and formal theory development. Proper execution of these elements is important for convincing reviewers and readers that the findings of the research are meaningful and trustworthy.Originality/valueThis paper should be of significant value to researchers who are interested in GT as a methodology. It adds to the few journal articles that address the proper ways to conduct GT.
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Grinbaum, Oleg. "Issues of Verse Theory: Aesthetic Categories and the Poetic Text." Respectus Philologicus 25, no. 30 (April 25, 2014): 118–39. http://dx.doi.org/10.15388/respectus.2014.25.30.9.
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This article discusses issues of verse theory as it relates to the stanza as a structural unit of a poetic text. The basic aesthetic categories (limits, harmony, grace, and beauty) are considered from the position of mathematical aesthetics, and a mathematical interpretation is offered for three of them (limits, harmony, and grace) in respect to the poetic text (stanza). The category “beauty” cannot correlate with formal descriptions, as far as beauty is the highest subjective-qualitative assessment of an observed object and formed on the basis of a quantitative-qualitative assessment of its limits, harmony, and grace. From the standpoint of aesthetic science, a verse represents the motion limits of a poetic thought. For the mathematical two new formal parameters are introduced, namely the “harmony” and “grace” of the poetic rhythm. In fact, these formal parameters are indicative correlates of expressive (sensual-meaningful) possibilities and kinds of artistic and poetic form (stanzas). In the network of mathematical aesthetics, new parameters acquire clear and mathematically precise definitions and computational procedures that make it possible to quantitatively assess the harmonic potential of different stanzas in their structural-systemic representation. The concept of a stanza’s harmonic profile is introduced, which allows very subtle differences to be captured in the aesthetic properties of different stanzas of Russian classical verse. The employment of new parameters is demonstrated through examples of the most productive of Pushkin’s stanzas.
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Northoff, Georg, Naotsugu Tsuchiya, and Hayato Saigo. "Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness." Entropy 21, no. 12 (December 17, 2019): 1234. http://dx.doi.org/10.3390/e21121234.
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Consciousness is a central issue in neuroscience, however, we still lack a formal framework that can address the nature of the relationship between consciousness and its physical substrates. In this review, we provide a novel mathematical framework of category theory (CT), in which we can define and study the sameness between different domains of phenomena such as consciousness and its neural substrates. CT was designed and developed to deal with the relationships between various domains of phenomena. We introduce three concepts of CT which include (i) category; (ii) inclusion functor and expansion functor; and, most importantly, (iii) natural transformation between the functors. Each of these mathematical concepts is related to specific features in the neural correlates of consciousness (NCC). In this novel framework, we will examine two of the major theories of consciousness, integrated information theory (IIT) of consciousness and temporospatial theory of consciousness (TTC). We conclude that CT, especially the application of the notion of natural transformation, highlights that we need to go beyond NCC and unravels questions that need to be addressed by any future neuroscientific theory of consciousness.
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Phillips, Steven. "Sheaving—a universal construction for semantic compositionality." Philosophical Transactions of the Royal Society B: Biological Sciences 375, no. 1791 (December 16, 2019): 20190303. http://dx.doi.org/10.1098/rstb.2019.0303.
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Semantic compositionality—the way that meanings of complex entities obtain from meanings of constituent entities and their structural relations—is supposed to explain certain concomitant cognitive capacities, such as systematicity. Yet, cognitive scientists are divided on mechanisms for compositionality: e.g. a language of thought on one side versus a geometry of thought on the other. Category theory is a field of (meta)mathematics invented to bridge formal divides. We focus on sheaving—a construction at the nexus of algebra and geometry/topology, alluding to an integrative view, to sketch out a category theory perspective on the semantics of compositionality. Sheaving is a universal construction for making inferences from local knowledge, where meaning is grounded by the underlying topological space. Three examples illustrate how topology conveys meaning, in terms of the inclusion relations between the open sets that constitute the space, though the topology is not regarded as the only source of semantic information. In this sense, category (sheaf) theory provides a general framework for semantic compositionality. This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.
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Hasan-Rokem, Galit. "Did Rabbinic Culture Conceive of the Category of Folk Narrative?" European Journal of Jewish Studies 3, no. 1 (2009): 19–55. http://dx.doi.org/10.1163/102599909x12471170467286.
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AbstractThe article addresses the question whether the late Antique Rabbinic texts disclose an awareness of the categories of folklore and folktale. Initially, the parallel and varied emergence of these categories in various intellectual traditions of modernity and post-modernity is presented with special reference to a new conceptual framework correlating the categories of magic, miracle and sorcery. Subsequently, the narrative traditions recounting the tales of Hanina ben Dosa and especially the chain of tales from the third chapter of the Babylonian Talmud tractate Ta'anit are presented and analyzed referring to earlier scholarship, manuscript variations and the conceptual framework of folk narratives and folklore. By analytically pointing out formal as well as contextual elements, a meta-folkloric awareness of the rabbis is argued.
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Caro, Daniel. "Stabilité de l’holonomie sur les variétés quasi-projectives." Compositio Mathematica 147, no. 6 (August 24, 2011): 1772–92. http://dx.doi.org/10.1112/s0010437x11005574.
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AbstractLet 𝒱 be a mixed characteristic complete discrete valuation ring with perfect residue field k. We solve Berthelot’s conjectures on the stability of the holonomicity over smooth projective formal 𝒱-schemes. Then we build a category of F-complexes of arithmetic 𝒟-modules over quasi-projective k-varieties with bounded and holonomic cohomology. We obtain its stability under Grothendieck’s six operations.
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Revtova, Elena. "Construction of the Definition of the “Credit” Category." Vestnik Volgogradskogo gosudarstvennogo universiteta. Ekonomika, no. 4 (February 2021): 122–31. http://dx.doi.org/10.15688/ek.jvolsu.2020.4.11.
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The subject of the research is the essence, nature and meaning of the “credit” category. The goal is to develop a definition of the “credit” category reflecting the nature of the phenomenon it refers to. Hypothesis: the author believes that general scientific research methods based on the idea of triadicity will reveal and describe the nature of the phenomenon of credit, as well as formulate a scientifically based definition of the corresponding category. Methods: formal-logical method, method of triadic decoding of categories. As a result of using the formallogical method the author defined: a) the generic concept “loan” as a universe, part of which is the “credit” category; b) non-credit forms of loans: “bill”, “bond”, “factoring”, “leasing”; c) necessary and sufficient conditions for classifying an object as a “credit”. A scientifically grounded definition of the “credit” category was formulated. As a result of deciphering the “credit” category, the essential qualities in the “credit” object, which together make up its essence, nature and meaning, were revealed; a detailed definition of the “credit” category was received. The research into the nature of credit has shown that the closest generic concept of credit is a loan; a necessary condition for classifying a credit as a loan is the transfer or receipt of money and goods on loan; repayment, payment and urgency are sufficient conditions for classifying a credit as a loan category; as a result, “credit” is defined as a kind of loan categories, the objective essential properties of which are repayment, payment and urgency. The field of applicability of the results in theory: the possibility of using the formal-logical method to investigate the nature of the research object; to check the obtained definition of the object for logical correctness; to enter your own definitions of the research object into the subject field with the help of “triads”. In lending practice the results are applicable as follows: scientifically grounded definition of the “credit” category, understanding the essence and nature of credit, its properties: repayment, payment and urgency to determine the specific variety of credit.
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BURSZTYN, HENRIQUE, and STEFAN WALDMANN. "*-IDEALS AND FORMAL MORITA EQUIVALENCE OF *-ALGEBRAS." International Journal of Mathematics 12, no. 05 (July 2001): 555–77. http://dx.doi.org/10.1142/s0129167x01000903.
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Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of *-algebras over a ring [Formula: see text] which is the quadratic extension by i of an ordered ring [Formula: see text]. The goal of the present paper is twofold. First, we clarify the relationship between formal Morita equivalence, Ara's notion of Morita *-equivalence of rings with involution, and strong Morita equivalence of C*-algebras. Second, in the general setting of *-algebras over [Formula: see text], we define "closed" *-ideals as the ones occurring as kernels of *-representations of these algebras on pre-Hilbert spaces. These ideals form a lattice which we show is invariant under formal Morita equivalence. This result, when applied to Pedersen ideals of C*-algebras, recovers the so-called Rieffel correspondence theorem. The triviality of the minimal element in the lattice of closed ideals, called the "minimal ideal", is also a formal Morita invariant and this fact can be used to describe a large class of examples of *-algebras over [Formula: see text] with equivalent representation theory but which are not formally Morita equivalent. We finally compute the closed *-ideals of some *-algebras arising in differential geometry.
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Putintsev, Andrey Vladimirovich. "System as a complex category of reflection of national security in theoretical-legal research." Национальная безопасность / nota bene, no. 1 (January 2021): 29–39. http://dx.doi.org/10.7256/2454-0668.2021.1.33825.
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The subject of this article is the methodology of reconstruction of national security as a complex social and political-legal phenomenon in modern scientific knowledge. Special attention is given to the provisions of the theory of state and law, political science, as well as official documents – the acts of strategic planning that are of theoretical and applied significance due to the presence of formal definitions in their texts. The article employs formal-legal and doctrinal analysis of scientific sources. Methodological framework is comprised of the category of “system” and systemic approach in various interpretations. Logical analysis is conducted on different variants of definitions of the category “national security system” and “system of ensuring national security”. It is revealed that systemic analysis, which historically is one of the most popular approaches that can reflect the multidimensional objects of research, has long been included into the scientific tradition of studying national security. The author explores several variants of systemic approach: the theory of national security as a system; national security as a system property; and national security as a system. The analysis of interpretation of national security as a system determines the two main categories: national security system and system of ensuring national security. The first category features mostly scientific interpretations, while the second category has received a legal definition, having transformed from the scientific category into an element of the object (social reality), and simultaneously, means of its construction. The author indicates the existence of methodological pluralism in determining the components of national security systems. The article examines successful and unsuccessful examples of application of systemic approach in studying national security, and identifies typical methodological errors. The author concludes on the limited heuristic possibilities of systemic approach in reflecting the dynamics of ensuring national security, as well as underlines the need to use the categories of “mechanism”, “regime"”, or “process”.
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GERKEN, MARK J. "SPECIFICATION OF SOFTWARE ARCHITECTURE." International Journal of Software Engineering and Knowledge Engineering 10, no. 01 (February 2000): 69–95. http://dx.doi.org/10.1142/s0218194000000067.
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Over the past several years, software architecture representation and analysis has become an active area of research. However, most approaches to software architecture representation and analysis have been informal. We postulate that through formality, the term "architecture" can be precisely defined and important properties of systems, such as semantic compatibility between connected entities, can be investigated with precision. In this paper, we use category theory and algebraic specifications to develop a formal definition of architecture and show how architecture theory can be used in the construction of software specifications.
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Li, Yizheng, and Dingguo Wang. "Lie algebras with differential operators of any weights." Electronic Research Archive 31, no. 3 (2022): 1195–211. http://dx.doi.org/10.3934/era.2023061.
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<abstract><p>In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.</p></abstract>
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Garbacz, Pawel. "What is an Artefact Design?" Techné: Research in Philosophy and Technology 13, no. 2 (2009): 137–49. http://dx.doi.org/10.5840/techne200913212.
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The paper contains a first order formal theory pertaining to artefact designs, designs which are construed as the results of designing activities. The theory is based on a minimal ontology of states of affairs and it is inspired by the ideas of the Polish philosopher Roman Ingarden. After differentiating the philosophical notion of design from the engineering notion of design specifications, I then go on to argue that the philosophical category of artefact designs may be compared with Ingarden’s category of intentional states of affairs. At least some artefacts are found to be determined by more than one design. I also show how this ontological framework allows for the distinction between artefact tokens and artefact types. That leads to a proposal on how to define a criterion of identity for artefact types. The proposed theory serves as a basis both for a better understanding of what artefacts are and for the construction of computer-readable models of design specifications.