Pull-Backs in Homotopy Theory

Abstract

The (based) homotopy category consists of (based) topological spaces and (based) homotopy classes of maps. In these categories, pull-backs and push-outs do not generally exist. For example, no essential map between Eilenberg-MacLane spaces of different dimensions has a kernel. In this paper we define homotopy pull-backs and push-outs, which do exist and which behave like pull-backs and push-outs, and we give some of their properties. Applications may be found in [3; 5; 6 and 14].