Natural dualities between abelian categories
Let \(\mathcal A\) and \(\mathcal B\) be abelian categories. Let \(F: \mathcal A\rightarrow \mathcal B\) and \(G:\mathcal B\rightarrow \mathcal A\) be a pair of right adjoint contravariant functors with natural transformations of right adjunction \(\delta:1_\mathcal A\rightarrow GF\) and \(\zeta:1_\mathcal B\rightarrow FG\). If \(C\) is a class of \(\delta\)-reflexive objects of \(\mathcal A\), and \(n\) is a positive integer, it is proved that \(F\) and \(G\) induce a duality between the category of all objects of \(\mathcal A\) with a \(n\)-dominant left \(C\)-resolution and the category of \(\zeta\)-reflexive objects of \(\mathcal B\) with a \(n\)-dominant right \(F(C)\)-resolution.
scientific article; zbMATH DE number 5997995
scientific article