Hopf Categories

被引:0
|
作者
E. Batista
S. Caenepeel
J. Vercruysse
机构
[1] Universidade Federal de Santa Catarina,Departamento de Matemática
[2] Vrije Universiteit Brussel,Faculty of Engineering
[3] Université Libre de Bruxelles,Département de Mathématique
来源
关键词
Enriched category; Hopf group coalgebra; Weak Hopf algebra; Duoidal category; Galois coobject; Morita context; Fundamental theorem; 16T05;
D O I
暂无
中图分类号
学科分类号
摘要
We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.
引用
收藏
页码:1173 / 1216
页数:43
相关论文
共 50 条
  • [1] Hopf Categories
    Batista, E.
    Caenepeel, S.
    Vercruysse, J.
    ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (05) : 1173 - 1216
  • [2] Hopf monads on categories
    Wisbauer, Robert
    NONCOMMUTATIVE RINGS, GROUP RINGS, DIAGRAM ALGEBRAS AND THEIR APPLICATIONS, 2008, 456 : 219 - 230
  • [3] HOPF POLYADS, HOPF CATEGORIES AND HOPF GROUP MONOIDS VIEWED AS HOPF MONADS
    Bohm, Gabriella
    THEORY AND APPLICATIONS OF CATEGORIES, 2017, 32 : 1229 - 1257
  • [4] On Hopf monoids in duoidal categories
    Boehm, Gabriella
    Chen, Yuanyuan
    Zhang, Liangyun
    JOURNAL OF ALGEBRA, 2013, 394 : 139 - 172
  • [5] Partial Hopf module categories
    Alvares, Edson R.
    Alves, Marcelo M. S.
    Batista, Eliezer
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (08) : 1517 - 1534
  • [6] Modular categories and Hopf algebras
    Takeuchi, M
    JOURNAL OF ALGEBRA, 2001, 243 (02) : 631 - 643
  • [7] Bimonads and Hopf monads on categories
    Mesablishvili, Bachuki
    Wisbauer, Robert
    JOURNAL OF K-THEORY, 2011, 7 (02) : 349 - 388
  • [8] Hopf monads on monoidal categories
    Bruguieres, Alain
    Lack, Steve
    Virelizier, Alexis
    ADVANCES IN MATHEMATICS, 2011, 227 (02) : 745 - 800
  • [9] (Hopf) Bimonoids in Duoidal Categories
    Bohm, Gabriella
    HOPF ALGEBRAS AND THEIR GENERALIZATIONS FROM A CATEGORY THEORETICAL POINT OF VIEW, 2018, 2226 : 99 - 123
  • [10] HOPF ALGEBRA ACTIONS IN TENSOR CATEGORIES
    Bischoff, M.
    Davydov, A.
    TRANSFORMATION GROUPS, 2021, 26 (01) : 69 - 80