Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs

Abstract

In this paper, we investigate the homotopy categories [Formula: see text] and [Formula: see text] with respect to a complete and hereditary cotorsion pair [Formula: see text] in a bicomplete abelian category. We prove that [Formula: see text] is compactly generated provided that [Formula: see text] is compactly generated. We introduce and characterize Gorenstein [Formula: see text]-complexes with respect to [Formula: see text] and show that a complex is a Gorenstein [Formula: see text]-complex if and only if its every term is a Gorenstein [Formula: see text]-object. We also show that the inclusion functors [Formula: see text] and [Formula: see text] have right adjoints respectively when [Formula: see text] is compactly generated.