Projectivity and subprojectivity domains in exact categories

Abstract

We generalize to exact categories some new perspectives on projectivity, which allow us to unify a series of recent concepts from module categories or abelian categories and to obtain automatically dual results. We discuss objects having a minimal subprojectivity domain in exact categories, and we study properties of such domains, including several closure properties. We give applications to (possibly non-abelian) quasi-abelian categories, finitely accessible and exactly definable additive categories, and in particular, to module and comodule categories.