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Chain complexes and stable categories. (English) Zbl 0753.18005
Supposing \(\mathcal A\) is an exact category with enough injectives, for any full additive subcategory \(\mathcal X\) of the stable category \(\underline{\mathcal A}\) one constructs an \(S\)-functor \({\mathcal H}_{0]}{\mathcal X}\to\underline{\mathcal A}\) extending the inclusion. (Here \({\mathcal H}_{0]}{\mathcal X}\) is the full subcategory of the homotopy category \(\mathcal H\mathcal X\) consisting of the positive chain complexes.) Applications to the case of some specific categories whose objects are obtained from finitely (countably) generated modules over a finite-dimensional \(k\)-algebra are considered.

18E30 Derived categories, triangulated categories (MSC2010)
18G35 Chain complexes (category-theoretic aspects), dg categories
18G10 Resolutions; derived functors (category-theoretic aspects)
18E10 Abelian categories, Grothendieck categories
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