Continuing this up to n-morphisms between (n−1)-morphisms gives an n-category. Representations of Algebras and Related Topics (2011), (Version arXiv). Title: Lifting (co)stratifications between tensor triangulated categories Authors: Liran Shaul, Jordan Williamson. 2, 138-149. In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. vol 11, 2007, pp 1539–1579, Arxiv; Topological conformal field theories and Calabi-Yau categories. aliases.json tells twXiv aliases of arXiv category names. A 2-category generalizes this by also including 2-morphisms between the 1-morphisms. Abstract . Pure Math. Generalization of general abstract nonsense (, "A Perspective on Higher Category Theory", https://en.wikipedia.org/w/index.php?title=Higher_category_theory&oldid=949884195, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 9 April 2020, at 02:30. The Grothendieck construction for model categories with Matan Prasma, Advances in Mathematics, 281, 2015, p. 1306-1363 (pdf, arXiv). 3; 場の量子論：幾何の量子化と量子代数; 木村太郎 Le style de jeu d'AlphaZero s'écarte des programmes de jeu habituels tout en requérant moins de calculs par mouvement en regard de ses concurrents [3], [4]. Just as the category known as Cat, which is the category of small categories and functors is actually a 2-category with natural transformations as its 2-morphisms, the category n-Cat of (small) n-categories is actually an (n+1)-category. stream If provided, twXiv replaces category names by their aliases … Any nite-dimensional algebra is Morita equivalent to a basic one, which is unique up to isomorphism. in Math. Cambridge University Press. of Math (2012), 23 (4) 1-23. 14, pp. arXiv est une archive ouverte de prépublications électroniques d'articles scientifiques dans les domaines de la physique, des mathématiques, de l'informatique, de la biologie quantitative, de la finance quantitative, de la statistique, de l'ingénierie électrique et des systèmes, et de l'économie [1], et qui est accessible gratuitement par Internet in Math. arXiv:2011.12501 (math) [Submitted on 25 Nov 2020] Title: Supersymmetric monoidal categories. Subjects: Category Theory (math.CT); K-Theory and Homology (math.KT); Representation Theory (math.RT) [2] arXiv:1609.02883 [ pdf , other ] Title: A Category Theoretical Investigation of the Type Hierarchy for Heterogeneous Sensor Integration A category has two basic properties: the ability to compose the arrows associatively, and the existence of an identity arrow for each object. nLab, the collective and open wiki notebook project on higher category theory and applications in physics, mathematics and philosophy; Joyal's Catlab, a wiki dedicated to polished expositions of categorical and higher categorical mathematics … A particularity of these is that a bicategory with one object is exactly a monoidal category, so that bicategories can be said to be "monoidal categories with many objects." The field for inserting MSC-classes doesn't ask separately for Primary and Secondary classifications, but the arXiv recommends the use of these. Soc. For Basic Category Theory (2014), the arrangement was that I could arXiv it one year after publication (I think a post-copyediting version, though I forget now). On generalized cluster categories, survey at Series of Congress Reports, Eur. S. X. Cui. arXiv: 1001.4071 . (With Nathan Geer and Bertrand Patureau) Journal of Topology (2014) . (with S.Brivio) arXiv Internat. For nearly 30 years, arXiv has served the public and research communities by providing open access to scholarly articles, from the vast branches of physics to the many subdisciplines of computer science to everything in between, including math, statistics, electrical engineering, quantitative biology, and economics. "Deligne categories as limits in rank and characteristic", submitted (2016) - arXiv "p-adic dimensions in symmetric tensor categories in characteristic p", with Pavel Etingof and Victor Ostrik (2015), to appear in Quantum Topology - arXiv "Stability and periodicity in the modular representation theory of symmetric groups" (2015), submitted - arXiv Tamar Debora Ziegler (en hébreu : תמר ציגלר; née en 1971) est une mathématicienne israélienne connue pour ses travaux en théorie ergodique, combinatoire et théorie des nombres.Elle occcupe la chaire Henry and Manya Noskwith de mathématiques à l'Institut Einstein de mathématiques (en) de l'université hébraïque de Jérusalem It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online. arXiv:1609.03023v1 [math.CT] 10 Sep 2016 Tannakian formalism for fiber functors over tensor categories Amir Jafari Mostafa Einollahzadeh October 3, 2018 Abstract In this paper we generalize Tannakian formalism to fiber functors over general tensor categories. Here, basic ... categories A and B are Morita equivalent if there is a DG-functor A !B such that the induced functor Dc(A ) !Dc(B) is an equivalence, or a zig-zag of such Journal of Knot Theory and Its Ramifications, vol. 2, 138-149. Likewise, if you upvote 10 articles with the word "hyperbolic" in the title, any other article with the word "hyperbolic" will gain 10 points. math.NA (Numerical Analysis) Numerical algorithms for problems in analysis and algebra, scientific computation The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. Instructions follow. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants of spaces, such as their fundamental weak ∞-groupoid. ... We introduce a construction called Clifford eversion that defines an equivalence between a certain 2-category of supersymmetric monoidal supercategories and a corresponding 2-category of symmetric monoidal supercategories. arXiv: math.CT/0608040. B. Antieau and G. Stevenson, Derived categories of representations of small categories over commutative noetherian rings, Pacific Journal of Mathematics 283 (2016), no. An example in topology is the composition of paths, where the identity and association conditions hold only up to reparameterization, and hence up to homotopy, which is the 2-isomorphism for this 2-category. 1750104, 2017. arXiv:1702.07113; Higher categories and topological quantum field theories. For example, math.IT is an alias of cs.IT. Malgré le découpage parfois un peu arbitraire (il y a une catégorie K-theorie et Homologie par exemple qui est assez spécifique) les catégories les plus fournies (je n'ai pas compté les maths app comme analyse numérique ou optimisation et controle ou la physique mathématiques) sont: 1. Two systems of coordinates to represent Boltzmann’s collision kernel. ... pp 1223-1234, 2012. Finally, we develop the theory of Frobenius-Perron dimensions in an arbitrary fusion category and classify categories of prime dimension. Associahedra ... Higher categories and geometric combinatorics of free groups. the category of compactly generated Hausdorff topological spaces. (2011) (Version arXiv). 119–140 - arXiv "Stability and periodicity in the modular representation theory of symmetric groups" (2015) - arXiv vol 210, 2007, pp 165–214, Arxiv; avec Claudia Scheimbauer: Lectures on mathematical aspects of (twisted) supersymmetric gauge theories. Lecture series in IPhT, CEA Saclay, 2015 [arXiv:1510.04430] 書籍. Monoidal categories enriched in braided monoidal categories. Equation aux dérivées partielles (336 prepublis) Unitary dual functors for unitary multitensor categories. Available on ArXiv: arXiv:1210.2666 ; Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories. "Homotopy theory of higher categories". Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms). Homotopy Theory of Higher Categories: From Segal Categories to N-Categories, Cambridge University Press, 2012 « The Hodge filtration on nonabelian cohomology », dans Algebraic Geometry Santa Cruz 1995, Part 2, coll. On generalized cluster categories, article de synthèse à Series of Congress Reports, Eur. Simpson, Carlos (2010). Higher Topos Theory. The monoidal structure of Set is the one given by the cartesian product as tensor and a singleton as unit. Subjects: Category Theory (math.CT); Rings and Algebras (math.RA); Representation Theory (math.RT) [2] arXiv:2007.04485 [ pdf , ps , other ] Title: Computing … These n-isomorphisms must well behave between hom-sets and expressing this is the difficulty in the definition of weak n-categories. x��[Ks�F�������a��sh��g{�m�xzccC�"!6 � h��~�Q�����΅(ꙕ�壒��a������Oo�x��l��*[}�_ ic�ʕ��8ˡj�����Z�Y�G����wo�D��7�_�Uf����ÕJ��n?��� ���l�ǹ�GLVk��\�P��Jfѯ�S°Q�uX(��W���a`�F�ms�66����$?&����O6��L�������ł� Z. Wang and S. X. Cui. Without this file, twXiv of rss feeds returns no new submissions, when you take the category name math.IT. Journ. Soc. See hal and arxiv. In: Adv. B. Antieau, On the integral Tate conjecture for finite fields and representation theory , Algebraic Geometry 3 (2016), no. 1, 21-42. Here, basic means that, as a right module, decomposes as = P 1 P n were each P i is indecomposable and P i˛P j for i6= j. Higher Operads, Higher Categories. AlphaGo est un programme informatique capable de jouer au jeu de go, développé par l'entreprise britannique Google DeepMind.. En octobre 2015, il devient le premier programme à battre un joueur professionnel (le français Fan Hui) sur un goban de taille normale (19×19) sans handicap. The same for other enriched models like topologically enriched categories. [arXiv:1509.00038] David Penneys. Math… Algebraic and Geometric Topology, 15 (4), 2015, p. 2303-2381 (pdf, arXiv). An n-category is defined by induction on n by: So a 1-category is just a (locally small) category. The data was not splited. (with M.Bernardara) arXiv Compositio Mathematica 149, n.11,1789-1817 (2013). But given that that was a textbook rather than a research work, I wasn’t in such a hurry to make a free version available. ����C}�#`M���W�_��Ѫ���33,n8��Q�u�r��y�-o���R�k�LO�v���� �As�����]2׀��ʱ,� q��d~u��դ��h�0P����r���'���&S��X������Z;�R��_�d#�l'�4>�@� ��N�����.ʖK ��%����P[}[���e����� ��b��z� �h�h�� ��}hJ�h��J�z��h�������9٠|=. Symp. arXiv admin note: text overlap with arXiv:1704.08764. Le 5 décembre 2017, DeepMind poste sur la plateforme de prépublication arXiv un article concernant AlphaZero [1], [2], un programme utilisant l’approche généralisée d'AlphaGo Zero. Weak 3-categories, also called tricategories, and higher-level generalizations are increasingly harder to define explicitly. Coherent systems and birational geometry of SU_C(r). The Geometry of maximal representations of surface groups into SO(2,n), avec Brian Collier et Jérémy Toulisse. Note: the published version is titled "Four … Forgetful linear systems on the projective space and rational normal curves over M_{0,2n}^{GIT} arXiv Bull. These are models of higher categories introduced by Hirschowitz and Simpson in 1998,[2] partly inspired by results of Graeme Segal in 1974. Compact components in relative character varieties of punctured spheres, avec Jérémy Toulisse. In fact any category with finite products can be given a monoidal structure. For example, if you click thumbs-up for 10 articles in the category "math.MG", then any article in the category "math.MG" will gain 10 points towards its computed score. Subjects: Category Theory (math.CT); Rings and Algebras (math.RA) [13] arXiv:2009.09273 (cross-list from math.OA) [ pdf , other ] Title: Standard $λ$-lattices, rigid ${\rm C}^*$ tensor categories… We then use this machinery to set up a general theory of 2-(co)limits for diagrams valued in an $\infty$-bicategory, capable of expressing lax, weighted and pseudo limits. "Deligne categories as limits in rank and characteristic" (2016) - arXiv "p-adic dimensions in symmetric tensor categories in characteristic p", with Pavel Etingof and Victor Ostrik, Quantum Topology, Volume 9, Issue 1, 2018, pp. Notices of the American Math Society, p7, Jan. 2014. The recursive construction of n-Cat works fine because if a category C has finite products, the category of C-enriched categories has finite products too. Congratulations, Tom! Int. However, when we look at them as a model for (infinity,1)-categories, then many categorical notions (e.g., limits) do not agree with the corresponding notions in the sense of enriched categories. Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms). As a moderator, I see every submission for which either the author lists cs.DM as one of its categories, or an admin/moderator proposes cs.DM as a new category. As PDF. About ArXiv. 1. Duke Mathematical Journal 168 (15), 2019, p. 2873-2949. arXiv:1702.08799. Nous avons ensuite introduit la structure de modèle sur les ensembles simpliciaux dont les objets fibrants sont les quasi-catégories. math.AG - Algebraic Geometry ( new , recent , current month ) Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology. Its purpose is to introduce triangulated categories related to singularities of algebraic varieties and establish a connection of these categories with D-branes in Landau-Ginzburg models. Draft of a book. Representations of Algebras and Related Topics (2011), (Version arXiv). We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. arXiv:1810.10068v4 [math.KT] 11 May 2020. [arXiv (soon) ] Extending the Tamari lattice to some compositions of species. ISBN 978-0-691-14048-3. Soc. math.MP is an alias for math-ph. arXiv:math/0607385v1 [math.AG] 17 Jul 2006 THÈSE résentée p p our le diplôme de do cteur de l'université oulouse T I I I aul P Sabatier en TIQUES THÉMA MA PURES r pa Mathieu Anel intitulée CHAMPS DE MODULES DES TÉGORIES CA LINÉAIRES ET ABÉLIENNES soutenue le 23 juin 2006 devant le jury comp osé de wrence La Breen Professeur, Univ. Structures 4 ( 2 ):22-56, 2020 ; categories n−1 ) gives! 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