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Deformation theory of abelian categories

Wenty T. Lowen·Michel Van den Bergh
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Abstract

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations and we construct several equivalences between deformation problems.

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Wenty T. Lowen, Michel Van den Bergh. 2004-05-12. Deformation theory of abelian categories. https://arxiv.org/abs/math/0405226

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