Deformation theory of objects in homotopy and derived categories I: general theory
arXiv:math/0702838 · doi:10.1016/j.aim.2009.03.021
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 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 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.
Alexander Efimov is a new co-author of this paper. Besides some minor changes, Proposition 7.1 and Theorem 8.1 were corrected
References in corpus (5)
- Lie theory for nilpotent L-infinity algebras
- Deformation theory of objects in homotopy and derived categories III: abelian categories
- Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
- Obstruction theory for objects in abelian and derived categories
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Cited by in corpus (10)
- Uniqueness of enhancement for triangulated categories
- Noncommutative deformations and flops
- Deformation theory of objects in homotopy and derived categories III: abelian categories
- Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
- Derived, coderived, and contraderived categories of locally presentable abelian categories
- Purity and 2-Calabi-Yau categories
- Cluster categories and rational curves
- The derived deformation theory of a point
- Non-commutative thickening of moduli spaces of stable sheaves
- Non-commutative derived moduli prestacks