ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT 2-CATEGORIES AND THEIR 2-REPRESENTATIONS
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 کامل2-Groups, trialgebras and their Hopf categories of representations
A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...
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: Journal of the Institute of Mathematics of Jussieu
سال: 2018
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748018000555