## 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.

### MSC:

 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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