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Deformation theory of objects in homotopy and derived categories I: general theory

Alexander I. Efimov·Valery A. Lunts·Dmitri O. Orlov
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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 defined on the category of artinian (not necessarily commutative) DG algebras.

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Alexander I. Efimov, Valery A. Lunts, Dmitri O. Orlov. 2008-09-15. Deformation theory of objects in homotopy and derived categories I: general theory. https://doi.org/10.1016/j.aim.2009.03.021

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