For hereditary complete cotorsion pairs generated by a set in a Grothendieck category, the coderived category of the left class is equivalent to the contraderived category of the right class, and for sandwiched pairs this flat-type behavior is equivalent to two periodicity properties.
Deconstructibility and the Hill lemma in Grothendieck categories
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abstract
A full subcategory of a Grothendieck category is called deconstructible if it consists of all transfinite extensions of some set of objects. This concept provides a handy framework for structure theory and construction of approximations for subcategories of Grothendieck categories. It also allows to construct model structures and t-structures on categories of complexes over a Grothendieck category. In this paper we aim to establish fundamental results on deconstructible classes and outline how to apply these in the areas mentioned above. This is related to recent work of Gillespie, Enochs, Estrada, Guil Asensio, Murfet, Neeman, Prest, Trlifaj and others.
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Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
For hereditary complete cotorsion pairs generated by a set in a Grothendieck category, the coderived category of the left class is equivalent to the contraderived category of the right class, and for sandwiched pairs this flat-type behavior is equivalent to two periodicity properties.