Georgios Dalezios

Induced abelian model structures on functor categories.

Abstract:

We consider the problem of lifting complete cotorsion pairs from an abelian category A to functor categories of the form [C,A] where C is a small (preadditive) category. This problem is parallel to the one of lifting (abelian) model structures. Answers to such questions heavily depend on the shape of the diagram, i.e. the category C. We survey some known cases (e.g. when C is a rooted quiver) and present some new ones (e.g. when C is of Reedy shape).