Academic literature on the topic 'Artin gluing'

The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction , computational effects , and type abstraction . We contribute a fresh “synthetic” take on program modules that treats modules as the fundamental constructs, in which the usual suspects of prior module calculi (kinds, constructors, dynamic programs) are rendered as derived notions in terms of a modal type-theoretic account of the phase distinction. We simplify the account of type abstraction (embodied in the generativity of module functors) through a lax modality that encapsulates computational effects, placing projectibility of module expressions on a type-theoretic basis. Our main result is a (significant) proof-relevant and phase-sensitive generalization of the Reynolds abstraction theorem for a calculus of program modules, based on a new kind of logical relation called a parametricity structure . Parametricity structures generalize the proof-irrelevant relations of classical parametricity to proof- relevant families, where there may be non-trivial evidence witnessing the relatedness of two programs—simplifying the metatheory of strong sums over the collection of types, for although there can be no “relation classifying relations,” one easily accommodates a “family classifying small families.” Using the insight that logical relations/parametricity is itself a form of phase distinction between the syntactic and the semantic, we contribute a new synthetic approach to phase separated parametricity based on the slogan logical relations as types , by iterating our modal account of the phase distinction. We axiomatize a dependent type theory of parametricity structures using two pairs of complementary modalities (syntactic, semantic) and (static, dynamic), substantiated using the topos theoretic Artin gluing construction. Then, to construct a simulation between two implementations of an abstract type, one simply programs a third implementation whose type component carries the representation invariant.

The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction , computational effects , and type abstraction . We contribute a fresh “synthetic” take on program modules that treats modules as the fundamental constructs, in which the usual suspects of prior module calculi (kinds, constructors, dynamic programs) are rendered as derived notions in terms of a modal type-theoretic account of the phase distinction. We simplify the account of type abstraction (embodied in the generativity of module functors) through a lax modality that encapsulates computational effects, placing projectibility of module expressions on a type-theoretic basis. Our main result is a (significant) proof-relevant and phase-sensitive generalization of the Reynolds abstraction theorem for a calculus of program modules, based on a new kind of logical relation called a parametricity structure . Parametricity structures generalize the proof-irrelevant relations of classical parametricity to proof- relevant families, where there may be non-trivial evidence witnessing the relatedness of two programs—simplifying the metatheory of strong sums over the collection of types, for although there can be no “relation classifying relations,” one easily accommodates a “family classifying small families.” Using the insight that logical relations/parametricity is itself a form of phase distinction between the syntactic and the semantic, we contribute a new synthetic approach to phase separated parametricity based on the slogan logical relations as types , by iterating our modal account of the phase distinction. We axiomatize a dependent type theory of parametricity structures using two pairs of complementary modalities (syntactic, semantic) and (static, dynamic), substantiated using the topos theoretic Artin gluing construction. Then, to construct a simulation between two implementations of an abstract type, one simply programs a third implementation whose type component carries the representation invariant.

We consider the following two properties of a functor F from a presheaf topos to the category of sets: (a) F preserves connected limits, and (b) the Artin glueing of F is again a presheaf topos. We show that these two properties are in fact equivalent. In the process, we develop a general technique for associating categorical properties of a category obtained by Artin glueing with preservation properties of the functor along which the glueing takes place. We also give a syntactic characterization of those monads on Set whose functor parts have the above properties, and whose units and multiplications are cartesian natural transformations.

This study aims to analyze the tensile strength of steel SS400 with carbon fiber layer thickness variation to the application framework of electric cars, as well as proving the existence of an increase in the strength of the material. The method used to collect data in this study is the experimental method. This study uses tensile testing. a test to refine to be paid out starting on 12 specimens with some variation the thickness of the carbon fibers layer. A gluing naturally occurring carbon fiber use resin. The test results show that the yield strength value of steel SS400 with a 1 mm layer of carbon fiber has a strength of 427,435 N/mm2, the specimen with a layer of 3 mm carbon fiber has a yield strength value of 606,956 N/mm2, and specimens with carbon fiber layer have a thickness of 7 mm yield strength value of 823,230 N/mm2, while on the specimen without using carbon fiber layer showed yield strength smallest value is 345,509 N/mm2. Carbon fiber layer thickness affects the yield strength value specimens SS400. The thicker the layer is given, the higher the yield strength values obtained. Simulation results of failure based on a static test with multiple speed variations, von misses stress value does not exceed the maximum yield strength of the material that is owned by the materials in steel material SS400 with this carbon fiber coating well tested for further testing of the resulting minimum safety factor has a good value or more than one value which means that the construction is declared safe or can be further tested.Penelitian ini bertujuan menganalisis kekuatan tarik baja SS400 dengan variasi ketebalan lapisan karbon fiber untuk aplikasi kerangka mobil listrik, serta membuktikan adanya peningkatan kekuatan pada material. Metode yang digunakan untuk pengumpulan data pada penelitian ini adalah metode eksperimen. Penelitian ini menggunakan pengujian tarik. Pengujian dilakukan pada 12 spesimen dengan beberapa variasi ketebalan lapisan karbon fiber. Perekatan serat karbon menggunakan resin. Hasil pengujian tarik memperlihatkan bahwa nilai yield strength baja SS400 dengan lapisan serat karbon 1 mm memiliki kekuatan 427,435 N/mm2, spesimen dengan lapisan karbon fiber 3 mm memiliki nilai yield strength 606,956 N/mm2, dan spesimen dengan lapisan karbon fiber ketebalan 5 mm memiliki nilai yield strength 823,230 N/mm2, sedangkan pada spesimen tanpa menggunakan lapisan serat karbon menunjukkan nilai yield strength yang paling kecil yaitu 345,509 N/mm2. Ketebalan lapisan karbon fiber berpengaruh terhadap nilai yield strength spesimen baja SS400. Semakin tebal lapisan yang diberikan, maka semakin tinggi pula nilai yield strength yang didapat. Hasil Simulasi kegagalan berdasarkan static test dengan beberapa variasi kecepatan, nilai von misses stress tidak melebihi batas maksimal kekuatan luluh (yield strength) yang dimiliki material dalam artian material baja SS400 dengan pelapisan karbon fiber ini layak diuji lebih lanjut begitu pun untuk hasil safety factor minimum yang dihasilkan memiliki nilai baik atau nilainya lebih dari satu yang artinya kontruksi dinyatakan aman atau dapat diuji lebih lanjut.

We present XTT, a version of Cartesian cubical type theory specialized for Bishop sets \`a la Coquand, in which every type enjoys a definitional version of the uniqueness of identity proofs. Using cubical notions, XTT reconstructs many of the ideas underlying Observational Type Theory, a version of intensional type theory that supports function extensionality. We prove the canonicity property of XTT (that every closed boolean is definitionally equal to a constant) using Artin gluing.

This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated subcategories to lift to a torsion torsion-free triple (TTF triple) of ambient triangulated categories with coproducts is proved. As a consequence, lifting of TTF triples is possible for recollements of stable categories of repetitive algebras or self-injective finite length algebras and recollements of bounded derived categories of separated Noetherian schemes. When, in addition, the outer subcategories in the recollement are derived categories of small linear categories the conditions from the criterion are sufficient to lift the recollement to a recollement of ambient triangulated categories up to equivalence. In the second part we use these results to study the problem of constructing silting sets in the central category of a recollement generating the t-structure glued from the silting t-structures in the outer categories. In the case of a recollement of bounded derived categories of Artin algebras we provide an explicit construction for gluing classical silting objects.

AbstractUsing methods of categorical fuzzy topology, the paper shows a relation between topological systems of S. Vickers and Artin glueing of M. Artin. Inspired by the problem of interrelations between algebra and topology, we show the necessary and sufficient conditions for the category, obtained by Artin glueing along an adjoint functor, to be (co)algebraic and (co)monadic, incorporating the respective result of G. Wraith. As a result, we confirm the algebraic nature of the category of topological systems, showing that it is monadic.

Abstract This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and shows how it can be adapted to unify definability and normalisation, yielding an extensional normalisation result. In the second part of the paper, the analysis is refined further by considering intensional Kripke relations (in the form of Artin–Wraith glueing) and shown to provide a function for normalising terms, casting normalisation by evaluation in the context of categorical glueing. The technical development includes an algebraic treatment of the syntax and semantics of the typed lambda calculus that allows the definition of the normalisation function to be given within a simply typed metatheory. A normalisation-by-evaluation program in a dependently typed functional programming language is synthesised.