What do Abelian categories form?. (1st February 2022)

• Record Type: Journal Article
• Authors: Kaledin, D. B.
• Is Part Of: Russian mathematical surveys. Volume 77:Number 1(2022)
• Page Start: 1
• Page End: 45
• Publication Date: 2022-02-01
• Subjects: 18E10; 18N10; Abelian category -- stable category -- 2-category -- Hochschild cohomology -- Mac Lane cohomology; Mathematics -- Soviet Union -- Periodicals; Mathematics -- Russia (Federation) -- Periodicals; Mathematics -- Periodicals; Mathematicians -- Soviet Union -- Periodicals; Mathematicians -- Russia (Federation) -- Periodicals; 510.5
• DOI: 10.1070/RM10044
• Languages: English
• ISSNs: 0036-0279

Abstract

Abstract: Given two finitely presentable Abelian categories and, we outline a construction of an Abelian category of functors from to, which has nice 2-categorical properties and provides an explicit model for a stable category of stable functors between the derived categories of and . The construction is absolute, so it makes it possible to recover not only Hochschild cohomology but also Mac Lane cohomology. Bibliography: 29 titles.