Locally finitely presented categories and functor rings

Abstract

By using the correspondence between locally finitely presented additive categories and rings with enough idempotents, we study several properties of such rings in terms of the associated categories, and conversely. In particular, it is shown that a ring $R$ (with enough idempotents) is right perfect and the categories of finitely presented right and left $R$-modules are dual to each other if and only if the categories of projective and of injective right $R$-modules are equivalent.