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Relevant bibliographies by topics / Monoidal categories

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Academic literature on the topic 'Monoidal categories'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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Journal articles on the topic "Monoidal categories"

1

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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2

Morrison, Scott, and David Penneys. "Monoidal Categories Enriched in Braided Monoidal Categories." International Mathematics Research Notices 2019, no. 11 (2017): 3527–79. http://dx.doi.org/10.1093/imrn/rnx217.

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Abstract We introduce the notion of a monoidal category enriched in a braided monoidal category $\mathcal{V}$. We set up the basic theory, and prove a classification result in terms of braided oplax monoidal functors to the Drinfeld centre of some monoidal category $\mathcal{T}$. Even the basic theory is interesting; it shares many characteristics with the theory of monoidal categories enriched in a symmetric monoidal category, but lacks some features. Of particular note, there is no cartesian product of braided-enriched categories, and the natural transformations do not form a 2-category, but

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3

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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Vallette, Bruno. "Free Monoid in Monoidal Abelian Categories." Applied Categorical Structures 17, no. 1 (2008): 43–61. http://dx.doi.org/10.1007/s10485-008-9130-y.

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ARDIZZONI, ALESSANDRO, and LAIACHI EL KAOUTIT. "INVERTIBLE BIMODULES, MIYASHITA ACTION IN MONOIDAL CATEGORIES AND AZUMAYA MONOIDS." Nagoya Mathematical Journal 225 (August 11, 2016): 1–63. http://dx.doi.org/10.1017/nmj.2016.25.

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In this paper we introduce and study Miyashita action in the context of monoidal categories aiming by this to provide a common framework of previous studies in the literature. We make a special emphasis of this action on Azumaya monoids. To this end, we develop the theory of invertible bimodules over different monoids (a sort of Morita contexts) in general monoidal categories as well as their corresponding Miyashita action. Roughly speaking, a Miyashita action is a homomorphism of groups from the group of all isomorphic classes of invertible subobjects of a given monoid to its group of automor

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6

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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7

Pastro, Craig, and Ross Street. "Weak Hopf monoids in braided monoidal categories." Algebra & Number Theory 3, no. 2 (2009): 149–207. http://dx.doi.org/10.2140/ant.2009.3.149.

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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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9

Balteanu, C., Z. Fiedorowicz, R. Schwänzl, and R. Vogt. "Iterated monoidal categories." Advances in Mathematics 176, no. 2 (2003): 277–349. http://dx.doi.org/10.1016/s0001-8708(03)00065-3.

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COCKETT, J. R. B., and J. S. LEMAY. "Integral categories and calculus categories." Mathematical Structures in Computer Science 29, no. 2 (2018): 243–308. http://dx.doi.org/10.1017/s0960129518000014.

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Differential categories are now an established abstract setting for differentiation. However, not much attention has been given to the process which is inverse to differentiation: integration. This paper presents the parallel development for integration by axiomatizing an integral transformation, sA: !A → !A ⊗ A, in a symmetric monoidal category with a coalgebra modality. When integration is combined with differentiation, the two fundamental theorems of calculus are expected to hold (in a suitable sense): a differential category with integration which satisfies these two theorems is called a c

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Dissertations / Theses on the topic "Monoidal categories"

1

Stanley, Donald. "Closed model categories and monoidal categories." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27731.pdf.

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2

Matsson, Isak. "Algebras in Monoidal Categories." Thesis, Uppsala universitet, Algebra och geometri, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-447430.

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3

Westrich, Quinton. "Lie Algebras in Braided Monoidal Categories." Thesis, Karlstad University, Faculty of Technology and Science, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-397.

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<p>We begin by recalling some basic definitions from Lie algebra theory to motivate our subsequent transition to the more general setting of category theory. Next, we develop a relatively self-contained introduction to those areas of category theory needed for an understanding of what follows. Here we also motivate and introduce the graphical calculus notations. We then state the definitions of a braided commutator algebra, a braided Lie algebra, and a braided commutator Lie algebra. We proceed to show that color Lie algebras and Lie superalgebras are examples of braided Lie algebras. Thus, we

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4

Fuller, Benjamin James. "Skew monoidal categories and Grothendieck's six operations." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/16499/.

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In this thesis, we explore several topics in the theory of monoidal and skew monoidal categories. In Chapter 3, we give definitions of dual pairs in monoidal categories, skew monoidal categories, closed skew monoidal categories and closed monoidal categories. In the case of monoidal and closed monoidal categories, there are multiple well-known definitions of a dual pair. We generalise these definitions to skew monoidal and closed skew monoidal categories. In Chapter 4, we introduce semidirect products of skew monoidal categories. Semidirect products of groups are a well-known and well-studied

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Schiavi, Andrea. "Monoidal categories for the physics of integrable models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7594/.

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Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

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Abdulwahid, Adnan Hashim. "Cofree objects in the categories of comonoids in certain abelian monoidal categories." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2032.

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We investigate cofree coalgebras, and limits and colimits of coalgebras in some abelian monoidal categories of interest, such as bimodules over a ring, and modules and comodules over a bialgebra or Hopf algebra. We nd concrete generators for the categories of coalgebras in these monoidal categories, and explicitly construct cofree coalgebras, products and limits of coalgebras in each case. This answers an open question in [4] on the existence of a cofree coring, and constructs the cofree (co)module coalgebra on a B-(co)mod

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Siehler, Jacob A. "Near-Group Categories." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/26962.

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We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, for the existence or nonexistence of coherent associative structures for such fusion rules (ie, solutions to MacLane's pentagon equation). An explicit construction of matrix solutions to the pentagon equations is given for the cases where we establish existence, and classification of the distinct so

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Ambler, Simon John. "First order linear logic in symmetric monoidal closed categories." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/11974.

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There has recently been considerable interest in the development of 'logical frameworks' which can represent many of the logics arising in computer science in a uniform way. Within the Edinburgh LF project, this concept is split into two components; the first being a general proof theoretic encoding of logics, and the second a uniform treatment of their model theory. This thesis forms a case study for the work on model theory. The models of many first and higher order logics can be represented as <i>fibred</i> or <i>indexed</i> categories with certain extra structure, and this has been suggest

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9

Balteanu, Cornel. "Coherence for iterated monoidal categories and homological obstructions to delooping /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487945744573181.

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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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Books on the topic "Monoidal categories"

1

Stanley, Donald. Closed model categories and monoidal categories. National Library of Canada = Bibliothèque nationale du Canada, 1997.

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2

Turaev, Vladimir, and Alexis Virelizier. Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8.

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1974-, Mahajan Swapneel Arvind, ed. Monoidal functors, species, and Hopf algebras. American Mathematical Society, 2010.

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4

Tensor categories. American Mathematical Society, 2015.

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5

Colored operads. American Mathematical Society, 2016.

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6

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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7

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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8

Separable algebroids. American Mathematical Society, 1985.

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9

1942-, Knauer U., and Mikhalev A. V, eds. Monoids, acts, and categories: With applications to wreath products and graphs : a handbook for students and researchers. W. de Gruyter, 2000.

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10

Stanley, Donald. Closed model categories and monoidal categories. 1997.

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Book chapters on the topic "Monoidal categories"

1

Hovey, Mark. "Monoidal model categories." In Model Categories. American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/063/04.

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2

Yau, Donald. "Involutive Monoidal Categories." In Lecture Notes in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61203-0_4.

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3

Turaev, Vladimir, and Alexis Virelizier. "Monoidal categories and functors." In Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_1.

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Turaev, Vladimir, and Alexis Virelizier. "Braided categories." In Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_3.

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Turaev, Vladimir, and Alexis Virelizier. "Fusion categories." In Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_4.

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6

Elias, Ben, Shotaro Makisumi, Ulrich Thiel, and Geordie Williamson. "How to Draw Monoidal Categories." In Introduction to Soergel Bimodules. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48826-0_7.

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7

Fresse, Benoit. "Symmetric monoidal categories for operads." In Modules over Operads and Functors. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89056-0_1.

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8

Yau, Donald. "Coherence of Involutive Monoidal Categories." In Lecture Notes in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61203-0_5.

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Turaev, Vladimir, and Alexis Virelizier. "Hopf algebras in braided categories." In Monoidal Categories and Topological Field Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_6.

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Fresse, Benoit. "Symmetric monoidal model categories for operads." In Modules over Operads and Functors. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89056-0_11.

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Conference papers on the topic "Monoidal categories"

1

Bernardy, Jean-Philippe, and Arnaud Spiwack. "Evaluating linear functions to symmetric monoidal categories." In ICFP '21: 26th ACM SIGPLAN International Conference on Functional Programming. ACM, 2021. http://dx.doi.org/10.1145/3471874.3472980.

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