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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
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.
Received: 20.09.2021
Citation:
D. B. Kaledin, “What do Abelian categories form?”, Russian Math. Surveys, 77:1 (2022), 1–45
Linking options:
https://www.mathnet.ru/eng/rm10044https://doi.org/10.1070/RM10044 https://www.mathnet.ru/eng/rm/v77/i1/p3
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Abstract page: | 753 | Russian version PDF: | 256 | English version PDF: | 115 | Russian version HTML: | 407 | References: | 92 | First page: | 42 |
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