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Littérature scientifique sur le sujet « Monoidal structure »

Auteur : Grafiati

Publié le 7 juin 2025

Mis à jour le 2 août 2025

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Articles de revues sur le sujet "Monoidal structure"

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Ma, Zizhu. "Generalized Enrichments of Categories for Operads." Algebra Colloquium 14, no. 01 (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

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DOŠEN, KOSTA, and ZORAN PETRIĆ. "Coherence for monoidal endofunctors." Mathematical Structures in Computer Science 20, no. 4 (2010): 523–43. http://dx.doi.org/10.1017/s0960129510000022.

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The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, that is, endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be an isomorphism. These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. In the later parts of the paper, the coherence results are extended to monoidal endofunctors in monoidal categories that have diagonal or codiagonal natural transformations, or where the monoidal structure is given by finite p

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Groth, Moritz, Kate Ponto, and Michael Shulman. "The additivity of traces in monoidal derivators." Journal of K-theory 14, no. 3 (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

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White, David, and Donald Yau. "Arrow categories of monoidal model categories." MATHEMATICA SCANDINAVICA 125, no. 2 (2019): 185–98. http://dx.doi.org/10.7146/math.scand.a-114968.

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We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, in the course of his work on Smith ideals. As a corollary, we prove that the projective model structure in cubical homotopy theory is a monoidal model structure. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, pro-categories, and topological spaces.

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DOŠEN, KOSTA, and ZORAN PETRIĆ. "Coherence for monoidal monads and comonads." Mathematical Structures in Computer Science 20, no. 4 (2010): 545–61. http://dx.doi.org/10.1017/s0960129510000034.

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The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, that is, monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor (this means that it preserves the monoidal structure up to a natural transformation that need not be an isomorphism). These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. The monoidal structure is also allowed to be given with finite products or finite coproducts. Monoidal comonads with finite

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Logar, Alessandro, and Fabio Rossi. "Monoidal closed structures on categories with constant maps." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (1985): 175–85. http://dx.doi.org/10.1017/s144678870002303x.

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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.

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Femic, Bojana. "Enrichment and internalization in tricategories, the case of tensor categories and alternative notion to intercategories." Filomat 38, no. 8 (2024): 2601–60. https://doi.org/10.2298/fil2408601f.

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This paper emerged as a result of tackling the following three issues. Firstly, we would like the well known embedding of bicategories into pseudo double categories to be monoidal, which it is not if one uses the usual notion of a monoidal pseudo double category. Secondly, in [3] the question was raised: which would be an alternative notion to intercategories of Grandis and Par?, so that monoids in B?hm?s monoidal category (Dbl,?) of strict double categories and strict double functors with a Gray type monoidal product be an example of it? We obtain and prove that precisely the monoidal structu

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BARNES, DAVID. "A monoidal algebraic model for rational SO(2)-spectra." Mathematical Proceedings of the Cambridge Philosophical Society 161, no. 1 (2016): 167–92. http://dx.doi.org/10.1017/s0305004116000219.

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AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal mod

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HASEGAWA, MASAHITO. "On traced monoidal closed categories." Mathematical Structures in Computer Science 19, no. 2 (2009): 217–44. http://dx.doi.org/10.1017/s0960129508007184.

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The structure theorem of Joyal, Street and Verity says that every traced monoidal category arises as a monoidal full subcategory of the tortile monoidal category Int. In this paper we focus on a simple observation that a traced monoidal category is closed if and only if the canonical inclusion from into Int has a right adjoint. Thus, every traced monoidal closed category arises as a monoidal co-reflexive full subcategory of a tortile monoidal category. From this, we derive a series of facts for traced models of linear logic, and some for models of fixed-point computation. To make the paper mor

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Joyal, André, Ross Street, and Dominic Verity. "Traced monoidal categories." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 3 (1996): 447–68. http://dx.doi.org/10.1017/s0305004100074338.

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Thèses sur le sujet "Monoidal structure"

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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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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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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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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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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 bla

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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 transfer

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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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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

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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 sy

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Livres sur le sujet "Monoidal structure"

1

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

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2

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. 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. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. American Mathematical Society, 2013.

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4

Subotic, Aleksandar. A monoidal structure for the Fukaya category. 2010.

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5

Colored operads. American Mathematical Society, 2016.

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6

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

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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 an

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

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Tensor categories. American Mathematical Society, 2015.

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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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Chapitres de livres sur le sujet "Monoidal structure"

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Hackney, Philip, Marcy Robertson, and Donald Yau. "Symmetric Monoidal Closed Structure on Properads." In Lecture Notes in Mathematics. 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. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-34827-3_2.

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Fukihara, Yōji, and Shin-ya Katsumata. "Generalized Bounded Linear Logic and its Categorical Semantics." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_12.

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AbstractWe introduce a generalization of Girard et al.’s called (and its affine variant ). It is designed to capture the core mechanism of dependency in , while it is also able to separate complexity aspects of . The main feature of is to adopt a multi-object pseudo-semiring as a grading system of the !-modality. We analyze the complexity of cut-elimination in , and give a translation from with constraints to with positivity axiom. We then introduce indexed linear exponential comonads (ILEC for short) as a categorical structure for interpreting the $${!}$$ ! -modality of . We give an elementar

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Kazhdan, D. "Meromorphic Monoidal Structures." In Lie Theory and Geometry. 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. 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. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12821-9_8.

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

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

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Selinger, P. "A Survey of Graphical Languages for Monoidal Categories." In New Structures for Physics. 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. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55511-0_21.

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Actes de conférences sur le sujet "Monoidal structure"

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Bonchi, Filippo, Fabio Gadducci, Aleks Kissinger, Paweł Sobociński, and Fabio Zanasi. "Rewriting modulo symmetric monoidal structure." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. 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. ACM Press, 2013. http://dx.doi.org/10.1145/2503778.2503785.

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Gong, C. M., Y. Q. Guo, and 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., and D. Therien. "Finite monoids and the fine structure of NC1." In the nineteenth annual ACM conference. ACM Press, 1987. http://dx.doi.org/10.1145/28395.28407.

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