Gorenstein projective objects in functor categories

2018/01/16 by Kvamme, Sondre
#16E65 #18E10 #18G25 #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1801.05493

Abstract

Let k be a commutative ring, let C be a small, k-linear, Hom-finite, locally bounded category, and let B be a k-linear abelian category. We construct a Frobenius exact subcategory GP(G_Pproj(B^C)) of the functor category B^C, and we show that it is a subcategory of the Gorenstein projective objects GP(B^C) in B^C. Furthermore, we obtain criteria for when GP(G_Pproj(B^C))=GP(B^C). We show in examples that this can be used to compute GP(B^C) explicitly.

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