Pull-Backs in Homotopy Theory
- 1 April 1976
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 28 (2) , 225-263
- https://doi.org/10.4153/cjm-1976-029-0
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].Keywords
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