Covering Functors, Skew Group Categories and Derived Equivalences

Abstract. Let G be a group of automorphisms of a category C. We give a definition for a functor F : C → C to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finitedimensional categories with group G whose action on C is free and locally bonded. Here C/G is defined for any category C and does not require that the action of G is free or locally bounded. We show that a G-covering is a universal “right G-invariant” functor and is essentially given by the canonical functor C → C/G. By using this we improve a covering technique for derived equivalence. In addition, we give a presentation of a skew monoid category by a quiver with relations, which enables us to calculate many examples.