Localizations of algebraic categories
The main result of the paper characterizes the localizations of concrete algebraic categories (= categories of Eilenberg-Moore algebras for a monad over \({\mathcal S}et\)) as the exact categories which have a regular generator admitting all copowers. It was known previously that the additional requirement of the regular generator being regular projective characterizes the concrete algebraic categories themselves, and that there also exists an easy characterization of the regular-epireflective subcategories and of all subcategories of concrete algebraic categories in this context. In proving his main result, the author makes essential use of the exact completion theory as presented in his work with \textit{A. Carboni} [``Regular and exact completions'', ibid. (to appear)].
scientific article; zbMATH DE number 897495