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Russian Mathematical Surveys, 2022, Volume 77, Issue 1, Pages 1–45
DOI: https://doi.org/10.1070/RM10044 (Mi rm10044) 		 
What do Abelian categories form?

D. B. Kaledinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Laboratory of Algebraic Geometry and its Applications, HSE University, Russian Federation
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DOI: https://doi.org/10.1070/RM10044
Abstract: Given two finitely presentable Abelian categories $A$ and $B$, we outline a construction of an Abelian category of functors from $A$ to $B$, which has nice 2-categorical properties and provides an explicit model for a stable category of stable functors between the derived categories of $A$ and $B$. The construction is absolute, so it makes it possible to recover not only Hochschild cohomology but also Mac Lane cohomology.
Bibliography: 29 titles.
Keywords: Abelian category, stable category, 2-category, Hochschild cohomology, Mac Lane cohomology.
Funding agency Grant number
Russian Science Foundation 21-11-00153
This work was supported by the Russian Science Foundation under grant no. 21-11-00153.
Received: 20.09.2021
Russian version:
Uspekhi Matematicheskikh Nauk, 2022, Volume 77, Issue 1(463), Pages 3–54
DOI: https://doi.org/10.4213/rm10044
Bibliographic databases:
Document Type: Article
UDC: 512.662
MSC: Primary 18E10; Secondary 18N10
Language: English
Original paper language: Russian
Citation: D. B. Kaledin, “What do Abelian categories form?”, Uspekhi Mat. Nauk, 77:1(463) (2022), 3–54; Russian Math. Surveys, 77:1 (2022), 1–45
Citation in format AMSBIB
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    References:92
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