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Deformation theory of abelian categories |
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| Authors: | Wendy Lowen Michel Van den Bergh |
| Institution: | Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium ; Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium |
| 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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