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.
Models for singularity categories
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abstract
In this article we construct various models for singularity categories of modules over differential graded rings. The main technique is the connection between abelian model structures, cotorsion pairs and deconstructible classes, and our constructions are based on more general results about localization and transfer of abelian model structures. We indicate how recollements of triangulated categories can be obtained model categorically, discussing in detail Krause's recollement for the stable derived category. In the special case of curved mixed Z-graded complexes, we show that one of our singular models is Quillen equivalent to Positselski's contraderived model for the homotopy category of matrix factorizations.
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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.