2020/10/22 by Wagstaffe, Rose
#13C60 (Secondary) #18E45 #18M05 (Primary) 16D90 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2010.12029
We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to the 2-category of fp-hom-closed definable additive categories satisfying an exactness criterion. For a fixed finitely accessible category C with products and a monoidal structure satisfying the appropriate assumptions, we provide bijections between the fp-hom-closed definable subcategories of C, the Serre tensor-ideals of Cfp\hbox-mod and the closed subsets of a Ziegler-type topology. For a skeletally small preadditive category A with an additive, symmetric, rigid monoidal structure we show that elementary duality induces a bijection between the fp-hom-closed definable subcategories of Mod\hbox-A and the definable tensor-ideals of A\hbox-Mod.