Bimorphisms in pro-homotopy and proper homotopy.

Abstract

A bimorphism is both an epimorphism and a monomorphism. If every bimorphism is an iso then the given category is said to be balanced. Such notions are studied in several contexts (pro-categories, pro-homotopy, shape, proper homotopy). The reference for pro-categories is [S. Mardesic and J. Segal, Shape theory (1982;]. The main results are related to the category towH0 where H0 is the homotopy category of pointed connected CW-complexes and towH0 is the full subcategory of pro-H0 constituted by the inverse sequences in H0.