Gorenstein versions of covering techniques for linear categories and their applications

Let C be a G-category for some group G. We show that a G-covering functor p:C⟶C/G induces G-precovering of their bounded derived categories, singularity categories and Gorenstein defect categories. Then we provide a Gorenstein version of Gabriel's theorem. Using this result we investigate the number of summands in a decomposition of the middle term of almost split sequences over monomial algebras.