# Deformation theory of objects in homotopy and derived categories I: General theory

@article{Efimov2009DeformationTO, title={Deformation theory of objects in homotopy and derived categories I: General theory}, author={Alexander I. Efimov and Valery A. Lunts and Dmitri O. Orlov}, journal={Advances in Mathematics}, year={2009}, volume={222}, pages={359-401} }

Abstract This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Def h ( E ) , coDef h ( E ) , Def ( E ) , coDef ( E ) . The first two functors describe the deformations (and co-deformations) of E in the homotopy category, and the last two – in the derived category. We study their properties and relations. These functors are… Expand

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Abstract This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation… Expand

Deformation theory of objects in homotopy and derived categories III: abelian categories

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Abstract This is the third paper in a series. In Part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to… Expand

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