Precover completing domains in exact categories

Abstract

Subprojectivity domains may be generalized to precover completing domains, not only in module categories, but also in additive (exact) categories. This is the setting in which we give several general properties of precover completing domains and we study objects having a minimal precover completing domain. We also prove some closure properties of precover completing domains, and we derive applications to finitely accessible categories and, in particular, to module categories.