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Pull-Backs in Homotopy Theory

Published online by Cambridge University Press:  20 November 2018

Michael Mather
Michael Mather*
Affiliation:
University of Toronto, Toronto, Ontario-, and University of Otago, Dunedin, New Zealand
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 225 - 263
Copyright
Copyright © Canadian Mathematical Society 1976

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