Deformation theory of abelian categories

Details Deformation theory of abelian categories Deformation theory of abelian categories

2004-05-12

arxiv.org/abs/math/0405226v1

Mathematics

Category Theory

44 pages

Scientific paper

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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