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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