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Groupoid Enriched Categories and Homotopy Theory

Published online by Cambridge University Press:  20 November 2018

P. H. H. Fantham  and
E. J. Moore
P. H. H. Fantham
Affiliation:
University of Toronto, Toronto, Ontario
E. J. Moore
Affiliation:
Scarborough College, University of Toronto, Scarborough, Ontario
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We are concerned in this paper with category-theoretic aspects of homotopy theory. Originally, category theory developed as a simplifying language in the context of algebraic topology and yet one primary example: the category Π of spaces and homotopy classes of maps admits only limited use of the language owing to the very sparse occurrence of limits. Of course, full use has been made of them nevertheless: limits and colimits exist in the case of products and coproducts, and in almost no other case; yet, from this we obtain the theory of Samelson products, Whitehead products, and Hopf invariants which can all be expressed in Π see [8]. In addition, there are hosts of adjoint functors and yet the outcome is disappointing because the language applies only to special cases rather than to the situation as a whole.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 3 , 01 June 1983 , pp. 385 - 416
Copyright
Copyright © Canadian Mathematical Society 1983

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