Regular and exact completions
This paper is devoted to the study of the regular and exact completions of categories with weak limits (the existence and uniqueness of these completions is proved) and to the characterization of categories which occur as such (an exact category is the exact completion, necessarily of its full subcategory of regular projectives iff it has enough projectives). Several examples (a category monadic over a power of \({\mathcal S}\)\textit{et} is the exact completion of the full subcategory of free algebras) and applications (to Grothendieck toposes and geometric morphisms, and to epireflective hulls) are also discussed.
scientific article; zbMATH DE number 1121676
scientific article