Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs
2018 ◽
Vol 17
(09)
◽
pp. 1850180
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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.
2011 ◽
Vol 54
(3)
◽
pp. 783-797
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Keyword(s):
2019 ◽
Vol 19
(08)
◽
pp. 2050142
2019 ◽
Vol 62
(3)
◽
pp. 564-583
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Keyword(s):
Keyword(s):