Categories with Strong Monomorphic Strong Coimages

Abstract

Let $SE(\mathcal{C})$ (respectively, $SM(\mathcal{C})$) be the subcategory of a category $\mathcal{C}$ with the same objects and whose morphisms are strong epimorphisms (respectively, strong monomorphisms) of $\mathcal{C}$. In this paper, we give conditions in some categories $\mathcal{C}$ for an object $X$ of pro-$\mathcal{C}$ to be isomorphic to an object of pro-$SE(\mathcal{C})$ (respectively, pro-$SM(\mathcal{C})$). As an application, we give conditions under which objects of pro-categories are stable.