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.
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves
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abstract
Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close connection of this theory to approximation theory and cotorsion pairs. We also discuss the motivating applications with the emphasis on constructing monoidal model structures for the derived category of quasi-coherent sheaves of modules over a scheme.
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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.