What do Abelian categories form?

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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.

About the authors

Dmitry Borisovich Kaledin

Steklov Mathematical Institute of Russian Academy of Sciences; Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE)

Email: kaledin@mi-ras.ru
Doctor of physico-mathematical sciences, no status

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