Additive versus abelian 2-Representations of Fiat 2-Categories
نویسندگان
چکیده
منابع مشابه
Additive versus Abelian 2-representations of Fiat 2-categories
We study connections between additive and abelian 2-representations of fiat 2-categories, describe combinatorics of 2-categories in terms of multisemigroups and determine the annihilator of a cell 2-representation. We also describe, in detail, examples of fiat 2-categories associated to sl2categorification in the sense of Chuang and Rouquier, and 2-categorical analogues of Schur algebras.
متن کاملIsotypic Faithful 2-representations of J -simple Fiat 2-categories
We introduce the class of isotypic 2-representations for finitary 2categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representations are equivalent to inflations of cell 2-representations.
متن کاملAbelian categories and definable additive categories
2 The category of small abelian categories and exact functors 4 2.1 Categorical properties of ABEX . . . . . . . . . . . . . . . . . . . 5 2.2 Pullbacks in ABEX . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 ABEX is finitely accessible . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Abelian categories as schemes . . . . . . . . . . . . . . . . . . . . 16 2.4.1 The functor of point...
متن کاملCell 2-representations of finitary 2-categories
We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by KazhdanLusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do no...
متن کاملTransitive 2-representations of Finitary 2-categories
In this article, we define and study the class of simple transitive 2-representations of finitary 2-categories. We prove a weak version of the classical Jordan-Hölder Theorem where the weak composition subquotients are given by simple transitive 2-representations. For a large class of finitary 2-categories we prove that simple transitive 2-representations are exhausted by cell 2-representations...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2014
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2014-14-3-595-615