Induced (E,M)−structures on Topological Categories

Abstract

In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms M and epimorphisms E for any topological category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some M−coreflective subcategories of a topological category. We pay special attention to projective structures.

Keywords

• (E,M)−category
• initial lift
• topological category
• topological functor