Bibliografie tematiche / Monoidal structures

Letteratura scientifica selezionata sul tema "Monoidal structures"

Autore: Grafiati

Pubblicato: 22 giugno 2024

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Articoli di riviste sul tema "Monoidal structures":

Riehl, Emily. "Monoidal algebraic model structures". Journal of Pure and Applied Algebra 217, n. 6 (giugno 2013): 1069–104. http://dx.doi.org/10.1016/j.jpaa.2012.09.029.

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Logar, Alessandro, e Fabio Rossi. "Monoidal closed structures on categories with constant maps". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, n. 2 (aprile 1985): 175–85. http://dx.doi.org/10.1017/s144678870002303x.

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Abstract (sommario):

AbstractThe purpose of this paper is to study the so-called canonical monoidal closed structures on concrete categories with constant maps. First of all we give an example of a category of this kind where there exists a non canonical monoidal closed structure. Later, we give a technique to construct a class of suitable full subcategories of the category of T0-spaces, such that all monoidal closed structures on them are canonical. Finally we show that “almost all” useful categories of topological compact spaces admit no monoidal closed structures whatsoever.

Schneider, Hans-Jürgen, e Blas Torrecillas. "Monoidal structures for N-complexes". Journal of Pure and Applied Algebra 223, n. 12 (dicembre 2019): 5083–90. http://dx.doi.org/10.1016/j.jpaa.2019.03.011.

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Mesablishvili, Bachuki. "Entwining structures in monoidal categories". Journal of Algebra 319, n. 6 (marzo 2008): 2496–517. http://dx.doi.org/10.1016/j.jalgebra.2007.08.030.

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García-Calcines, José Manuel, Luis Javier Hernández-Paricio e María Teresa Rivas-Rodríguez. "Augmented Simplicial Combinatorics through Category Theory: Cones, Suspensions and Joins". Mathematics 10, n. 4 (14 febbraio 2022): 590. http://dx.doi.org/10.3390/math10040590.

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In this work, we analyze the combinatorial properties of the category of augmented semi-simplicial sets. We consider various monoidal structures induced by the co-product, the product, and the join operator in this category. In addition, we also consider monoidal structures on augmented sequences of integers induced by the sum and product of integers and by the join of augmented sequences. The cardinal functor that associates to each finite set X its cardinal |X| induces the sequential cardinal that associates to each augmented semi-simplicial finite set X an augmented sequence |X|n of non-negative integers. We prove that the sequential cardinal functor is monoidal for the corresponding monoidal structures. This allows us to easily calculate the number of simplices of cones and suspensions of an augmented semi-simplicial set as well as other augmented semi-simplicial sets which are built by joins. In this way, the monoidal structures of the augmented sequences of numbers may be thought of as an algebraization of the augmented semi-simplicial sets that allows us to do a simpler study of the combinatorics of the augmented semi-simplicial finite sets.

Kelly, G. M., e F. Rossi. "Topological categories with many symmetric monoidal closed structures". Bulletin of the Australian Mathematical Society 31, n. 1 (febbraio 1985): 41–59. http://dx.doi.org/10.1017/s0004972700002264.

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Abstract (sommario):

It would seem from results of Foltz, Lair, and Kelly that symmetric monoidal closed structures, and even monoidal biclosed ones, are quite rare on one-sorted algebraic or essentially-algebraic categories. They showed many such categories to admit no such structures at all, and others to admit only one or two; no such category is known to admit an infinite set of such structures.Among concrete categories, topological ones are in some sense at the other extreme from essentially-algebraic ones; and one is led to ask whether a topological category may admit many such structures. On the category of topological spaces itself, only one such structure - in fact symmetric - is known; although Greve has shown it to admit a proper class of monoidal closed structures. One of our main results is a proof that none of these structures described by Greve, except the classical one, is biclosed.Our other main result is that, nevertheless, there exist topological categories (of quasi-topological spaces) which admit a proper class of symmetric monoidal closed structures. Even if we insist (like most authors) that topological categories must be wellpowered, we can still exhibit ones with more such structures than any small cardinal.

Bulacu, D., S. Caenepeel e B. Torrecillas. "The braided monoidal structures on the category of vector spaces graded by the Klein group". Proceedings of the Edinburgh Mathematical Society 54, n. 3 (14 giugno 2011): 613–41. http://dx.doi.org/10.1017/s0013091509001746.

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AbstractLet k be a field, let k* = k \ {0} and let C2 be a cyclic group of order 2. We compute all of the braided monoidal structures on the category of k-vector spaces graded by the Klein group C2 × C2. For the monoidal structures we compute the explicit form of the 3-cocycles on C2 × C2 with coefficients in k*, while, for the braided monoidal structures, we compute the explicit form of the abelian 3-cocycles on C2 × C2 with coefficients in k*. In particular, this will allow us to produce examples of quasi-Hopf algebras and weak braided Hopf algebras with underlying vector space k[C2 × C2].

Dorta, Joseph, Samantha Jarvis e Nelson Niu. "Monoidal Structures on Generalized Polynomial Categories". Electronic Proceedings in Theoretical Computer Science 397 (14 dicembre 2023): 84–97. http://dx.doi.org/10.4204/eptcs.397.6.

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Groth, Moritz, Kate Ponto e Michael Shulman. "The additivity of traces in monoidal derivators". Journal of K-theory 14, n. 3 (14 luglio 2014): 422–94. http://dx.doi.org/10.1017/is014005011jkt262.

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AbstractMotivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be “additive”. When the category is “stable” in some sense, additivity along cofiber sequences is a question about the interaction of stability and the monoidal structure.May proved such an additivity theorem when the stable structure is a triangulation, based on new axioms for monoidal triangulated categories. in this paper we use stable derivators instead, which are a different model for “stable homotopy theories”. We define and study monoidal structures on derivators, providing a context to describe the interplay between stability and monoidal structure using only ordinary category theory and universal properties. We can then perform May's proof of the additivity of traces in a closed monoidal stable derivator without needing extra axioms, as all the needed compatibility is automatic.

ESTRADA, SERGIO, JAMES GILLESPIE e SINEM ODABAŞI. "Pure exact structures and the pure derived category of a scheme". Mathematical Proceedings of the Cambridge Philosophical Society 163, n. 2 (23 novembre 2016): 251–64. http://dx.doi.org/10.1017/s0305004116000980.

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AbstractLet$\mathcal{C}$be closed symmetric monoidal Grothendieck category. We define the pure derived category with respect to the monoidal structure via a relative injective model category structure on the categoryC($\mathcal{C}$) of unbounded chain complexes in$\mathcal{C}$. We use λ-Purity techniques to get this. As application we define the stalkwise pure derived category of the category of quasi–coherent sheaves on a quasi-separated scheme. We also give a different approach by using the category of flat quasi–coherent sheaves.

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Tesi sul tema "Monoidal structures":

Espalungue, d'Arros Sophie d'. "Operads in 2-categories and models of structure interchange". Electronic Thesis or Diss., Université de Lille (2022-....), 2023. http://www.theses.fr/2023ULILB053.

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Le but de cette thèse est de fournir une construction explicite d'une résolution cofibrante des opérades de Balteanu-Fiedorowicz-Schwänzl-Vogt M_n, qui régissent les catégories monoidales itérées.Dans une première partie de la thèse, nous examinons en détail la définition des structures monoïdales dans les 2-catégories, ainsi que la définition des opérades dans les 2-catégories monoïdales, en prenant la 2-catégorie des catégories comme exemple principal. Ensuite, nous démontrons que la catégorie des opérades dans la catégorie des petites catégories hérite d'une structure de modèle par transfert de la structure de modèle folk sur la catégorie des petites catégories. Nous introduisons une notion de présentation polygraphique des opérades dans la catégorie des petites catégories afin de définir des opérades en terme de générateurs et relations à la fois dans la direction opératique et dans la direction catégorique au niveau des morphismes. Nous réexaminons la définition des opérades M_n en termes de présentations polygraphiques, et nous donnons une présentation de l'opérade M_1^infinity qui fournit une résolution cofibrante de l'opérade M_1 dans la structure de modèle folk. Enfin, nous étudions une généralisation du produit tensoriel de Boardman-Vogt dans le contexte des opérades dans la catégorie des catégories. Nous utilisons cette construction pour fournir une résolution cofibrante M_n^infinity de l'opérade M_n à partir de la résolution M_1^infinity de M_1, et ainsi répondre à la question initiale de la thèse
The goal of this thesis is to give an effective construction of a cofibrant resolution of the Balteanu-Fiedorowicz-Schwänzl-Vogt operads M_n, which govern iterated monoidal categories.In a first part of the thesis, we study thoroughly the definition of monoidal structures in 2-categories, and the definition of operads in monoidal 2-categories, with the 2-category of categories as a main motivating example. Then we prove that the category of operads in the category of small categories inherits a model structure by transfer of the folk model structure on the category of small categories. We introduce a notion of polygraphic presentation of operads in the category of small categories in order to define operads with generators and relations in both the operadic direction and the categorical direction at the morphism level. We revisit the definition of the operads M_n in terms of polygraphic presentations, and we gives a presentation of an operad M_1^infinity that provides a cofibrant resolution of the operad M_1 in the folk modelstructure. Eventually, we study a generalization of the Boardman-Vogt tensor product in the context of operads in the category of small categories. We use this construction to provide a cofibrant resolution M_n^infinity of the operad M_n from the resolution M_1^infinity of M_1, and hence, to address the initial question of the thesis

Reischuk, Rebecca [Verfasser]. "The monoidal structure on strict polynomial functors / Rebecca Reischuk". Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/110564555X/34.

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Staten, Corey. "Structure diagrams for symmetric monoidal 3-categories: a computadic approach". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1525455392722049.

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Aquilino, Cosima [Verfasser]. "On strict polynomial functors: monoidal structure and Cauchy filtration / Cosima Aquilino". Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/110754064X/34.

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Kunhardt, Walter. "On infravacua and the superselection structure of theories with massless particles". Doctoral thesis, [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962816159.

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Aquilino, Cosima [Verfasser]. "On strict polynomial functors: monoidal structure and Cauchy filtration. (Ergänzte Version) / Cosima Aquilino". Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://nbn-resolving.de/urn:nbn:de:hbz:361-29054451.

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Li, Zhuo. "Orbit structure of finite and reductive monoids". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21301.pdf.

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Zeng, William J. "The abstract structure of quantum algorithms". Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:cace8fba-b533-42f7-b9fd-959f2412c2a7.

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Abstract (sommario):

Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances foundations and practical applications of quantum information. Our first set of results analyze quantum algorithms with a process theoretic structure. We contribute new constructions of the Fourier transform and Pontryagin duality in dagger symmetric monoidal categories. We then use this setting to study generalized unitary oracles and give a new quantum blackbox algorithm for the identification of group homomorphisms, solving the GROUPHOMID problem. In the remaining section, we construct a novel model of quantum blackbox algorithms in non-deterministic classical computation. Our second set of results concerns quantum foundations. We complete work begun by Coecke et al., definitively connecting the Mermin non-locality of a process theory with a simple algebraic condition on that theory's phase groups. This result allows us to offer new experimental tests for Mermin non-locality and new protocols for quantum secret sharing. In our final chapter, we exploit the shared process theoretic structure of quantum information and distributional compositional linguistics. We propose a quantum algorithm adapted from Weibe et al. to classify sentences by meaning. The clarity of the process theoretic setting allows us to recover a speedup that is lost in the naive application of the algorithm. The main mathematical tools used in this thesis are group theory (esp. Fourier theory on finite groups), monoidal category theory, and categorical algebra.

Emtander, Eric. "Chordal and Complete Structures in Combinatorics and Commutative Algebra". Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-48241.

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This thesis is divided into two parts. The first part is concerned with the commutative algebra of certain combinatorial structures arising from uniform hypergraphs. The main focus lies on two particular classes of hypergraphs called chordal hypergraphs and complete hypergraphs, respectively. Both these classes arise naturally as generalizations of the corresponding well known classes of simple graphs. The classes of chordal and complete hypergraphs are introduced and studied in Chapter 2 and Chapter 3 respectively. Chapter 4, that is the content of \cite{E5}, answers a question posed at the P.R.A.G.MAT.I.C. summer school held in Catania, Italy, in 2008. In Chapter 5 we study hypergraph analogues of line graphs and cycle graphs. Chapter 6 is concerned with a connectedness notion for hypergraphs and in Chapter 7 we study a weak version of shellability.The second part is concerned with affine monoids and their monoid rings. Chapter 8 provide a combinatorial study of a class of positive affine monoids that behaves in some sense like numerical monoids. Chapter 9 is devoted to the class of numerical monoids of maximal embedding dimension. A combinatorial description of the graded Betti numbers of the corresponding monoid rings in terms of the minimal generators of the monoids is provided. Chapter 10 is concerned with monomial subrings generated by edge sets of complete hypergraphs.

Gay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.

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La combinatoire algébrique est le champ de recherche qui utilise des méthodes combinatoires et des algorithmes pour étudier les problèmes algébriques, et applique ensuite des outils algébriques à ces problèmes combinatoires. L’un des thèmes centraux de la combinatoire algébrique est l’étude des permutations car elles peuvent être interprétées de bien des manières (en tant que bijections, matrices de permutations, mais aussi mots sur des entiers, ordre totaux sur des entiers, sommets du permutaèdre…). Cette riche diversité de perspectives conduit alors aux généralisations suivantes du groupe symétrique. Sur le plan géométrique, le groupe symétrique engendré par les transpositions élémentaires est l’exemple canonique des groupes de réflexions finis, également appelés groupes de Coxeter. Sur le plan monoïdal, ces même transpositions élémentaires deviennent les opérateurs du tri par bulles et engendrent le monoïde de 0-Hecke, dont l’algèbre est la spécialisation à q=0 de la q-déformation du groupe symétrique introduite par Iwahori. Cette thèse se consacre à deux autres généralisations des permutations. Dans la première partie de cette thèse, nous nous concentrons sur les matrices de permutations partielles, en d’autres termes les placements de tours ne s’attaquant pas deux à deux sur un échiquier carré. Ces placements de tours engendrent le monoïde de placements de tours, une généralisation du groupe symétrique. Dans cette thèse nous introduisons et étudions le 0-monoïde de placements de tours comme une généralisation du monoïde de 0-Hecke. Son algèbre est la dégénérescence à q=0 de la q-déformation du monoïde de placements de tours introduite par Solomon. On étudie par la suite les propriétés monoïdales fondamentales du 0-monoïde de placements de tours (ordres de Green, propriété de treillis du R-ordre, J-trivialité) ce qui nous permet de décrire sa théorie des représentations (modules simples et projectifs, projectivité sur le monoïde de 0-Hecke, restriction et induction le long d’une fonction d’inclusion).Les monoïdes de placements de tours sont en fait l’instance en type A de la famille des monoïdes de Renner, définis comme les complétés des groupes de Weyl (c’est-à-dire les groupes de Coxeter cristallographiques) pour la topologie de Zariski. Dès lors, dans la seconde partie de la thèse nous étendons nos résultats du type A afin de définir les monoïdes de 0-Renner en type B et D et d’en donner une présentation. Ceci nous conduit également à une présentation des monoïdes de Renner en type B et D, corrigeant ainsi une présentation erronée se trouvant dans la littérature depuis une dizaine d’années. Par la suite, nous étudions comme en type A les propriétés monoïdales de ces nouveaux monoïdes de 0-Renner de type B et D : ils restent J-triviaux, mais leur R-ordre n’est plus un treillis. Cela ne nous empêche pas d’étudier leur théorie des représentations, ainsi que la restriction des modules projectifs sur le monoïde de 0-Hecke qui leur est associé. Enfin, la dernière partie de la thèse traite de différentes généralisations des permutations. Dans une récente séries d’articles, Châtel, Pilaud et Pons revisitent la combinatoire algébrique des permutations (ordre faible, algèbre de Hopf de Malvenuto-Reutenauer) en terme de combinatoire sur les ordres partiels sur les entiers. Cette perspective englobe également la combinatoire des quotients de l’ordre faible tels les arbres binaires, les séquences binaires, et de façon plus générale les récents permutarbres de Pilaud et Pons. Nous généralisons alors l’ordre faibles aux éléments des groupes de Weyl. Ceci nous conduit à décrire un ordre sur les sommets des permutaèdres, associaèdres généralisés et cubes dans le même cadre unifié. Ces résultats se basent sur de subtiles propriétés des sommes de racines dans les groupes de Weyl qui s’avèrent ne pas fonctionner pour les groupes de Coxeter qui ne sont pas cristallographiques
Algebraic combinatorics is the research field that uses combinatorial methods and algorithms to study algebraic computation, and applies algebraic tools to combinatorial problems. One of the central topics of algebraic combinatorics is the study of permutations, interpreted in many different ways (as bijections, permutation matrices, words over integers, total orders on integers, vertices of the permutahedron…). This rich diversity of perspectives leads to the following generalizations of the symmetric group. On the geometric side, the symmetric group generated by simple transpositions is the canonical example of finite reflection groups, also called Coxeter groups. On the monoidal side, the simple transpositions become bubble sort operators that generate the 0-Hecke monoid, whose algebra is the specialization at q=0 of Iwahori’s q-deformation of the symmetric group. This thesis deals with two further generalizations of permutations. In the first part of this thesis, we first focus on partial permutations matrices, that is placements of pairwise non attacking rooks on a n by n chessboard, simply called rooks. Rooks generate the rook monoid, a generalization of the symmetric group. In this thesis we introduce and study the 0-Rook monoid, a generalization of the 0-Hecke monoid. Its algebra is a proper degeneracy at q = 0 of the q-deformed rook monoid of Solomon. We study fundamental monoidal properties of the 0-rook monoid (Green orders, lattice property of the R-order, J-triviality) which allow us to describe its representation theory (simple and projective modules, projectivity on the 0-Hecke monoid, restriction and induction along an inclusion map).Rook monoids are actually type A instances of the family of Renner monoids, which are completions of the Weyl groups (crystallographic Coxeter groups) for Zariski’s topology. In the second part of this thesis we extend our type A results to define and give a presentation of 0-Renner monoids in type B and D. This also leads to a presentation of the Renner monoids of type B and D, correcting a misleading presentation that appeared earlier in the litterature. As in type A we study the monoidal properties of the 0-Renner monoids of type B and D : they are still J-trivial but their R-order are not lattices anymore. We study nonetheless their representation theory and the restriction of projective modules over the corresponding 0-Hecke monoids. The third part of this thesis deals with different generalizations of permutations. In a recent series of papers, Châtel, Pilaud and Pons revisit the algebraic combinatorics of permutations (weak order, Malvenuto-Reutenauer Hopf algebra) in terms of the combinatorics of integer posets. This perspective encompasses as well the combinatorics of quotients of the weak order such as binary trees, binary sequences, and more generally the recent permutrees of Pilaud and Pons. We generalize the weak order on the elements of the Weyl groups. This enables us to describe the order on vertices of the permutahedra, generalized associahedra and cubes in the same unified context. These results are based on subtle properties of sums of roots in Weyl groups, and actually fail for non-crystallographic Coxeter groups

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Libri sul tema "Monoidal structures":

Yau, Donald Y. Colored operads. Providence, Rhode Island: American Mathematical Society, 2016.

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Milner, Robin. Action structures for the (pi)-calculus. Edinburgh: LFCS, Dept. of Computer Science, University of Edinburgh, 1993.

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Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. Providence, Rhode Island: American Mathematical Society, 2015.

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Etingof, P. I., Shlomo Gelaki, Dmitri Nikshych e Victor Ostrik. Tensor categories. Providence, Rhode Island: American Mathematical Society, 2015.

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Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. A cura di Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975- e Torrecillas B. (Blas) 1958-. Providence, Rhode Island: American Mathematical Society, 2013.

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Heunen, Chris, e Jamie Vicary. Categories for Quantum Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198739623.001.0001.

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Abstract (sommario):

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures and Hopf algebras, showing how they can be used to model classical information and complementary observables. We describe the CP construction, a categorical tool to describe probabilistic quantum systems. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Previous knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text, we point out links with many other areas, such as representation theory, topology, quantum algebra, knot theory and probability theory, and present nonstandard models including sets and relations. All results are stated rigorously and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.

Gelaki, Shlomo, Dmitri Nikshych, Pavel Etingof e Victor Ostrik. Tensor Categories. American Mathematical Society, 2016.

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Tabuada, Gonçalo. Noncommutative Motives. American Mathematical Society, 2015.

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Advances In Ultrametric Analysis 12th International Conference On Padic Functional Analysis July 26 2012 University Of Manitoba Winnipeg Canada. American Mathematical Society, 2013.

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Capitoli di libri sul tema "Monoidal structures":

Kazhdan, D. "Meromorphic Monoidal Structures". In Lie Theory and Geometry, 489–95. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0261-5_17.

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Levine, Marc. "Symmetric monoidal structures". In Mixed Motives, 375–99. Providence, Rhode Island: American Mathematical Society, 1998. http://dx.doi.org/10.1090/surv/057/09.

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Lambek, J. "Compact Monoidal Categories from Linguistics to Physics". In New Structures for Physics, 467–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12821-9_8.

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Badouel, Eric, e Jules Chenou. "Nets Enriched over Closed Monoidal Structures". In Applications and Theory of Petri Nets 2003, 64–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44919-1_8.

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Selinger, P. "A Survey of Graphical Languages for Monoidal Categories". In New Structures for Physics, 289–355. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12821-9_4.

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Zhang, Guo-Qiang. "A monoidal closed category of event structures". In Lecture Notes in Computer Science, 426–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55511-0_21.

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Czaja, Ludwik. "Monoid of Processes". In Cause-Effect Structures, 97–103. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20461-7_11.

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Hackney, Philip, Marcy Robertson e Donald Yau. "Symmetric Monoidal Closed Structure on Properads". In Lecture Notes in Mathematics, 69–98. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20547-2_4.

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Pavlovic, Dusko. "Monoidal Computer: Computability as a Structure". In Programs as Diagrams, 25–54. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-34827-3_2.

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Dvurečenskij, Anatolij, e Sylvia Pulmannová. "Quotients of Partial Abelian Monoids". In New Trends in Quantum Structures, 191–229. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-2422-7_4.

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Atti di convegni sul tema "Monoidal structures":

Bonchi, Filippo, Fabio Gadducci, Aleks Kissinger, Paweł Sobociński e Fabio Zanasi. "Rewriting modulo symmetric monoidal structure". In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2935316.

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BlaĚević, Mario. "Adding structure to monoids". In the 2013 ACM SIGPLAN symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2503778.2503785.

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Gong, C. M., Y. Q. Guo e X. M. Ren. "A Structure Theorem for Ortho-u-monoids". In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0017.

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Barrington, D., e D. Therien. "Finite monoids and the fine structure of NC1". In the nineteenth annual ACM conference. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/28395.28407.

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