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