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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A homotopy theory of pro-spaces


Author: Jerrold W. Grossman
Journal: Trans. Amer. Math. Soc. 201 (1975), 161-176
MSC: Primary 55D05
DOI: https://doi.org/10.1090/S0002-9947-1975-0356039-8
MathSciNet review: 0356039
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Abstract: The category of towers of spaces, $ \ldots \to {X_{s + 1}} \to {X_s} \to \ldots \to {X_0}$, viewed as pro-spaces, appears to be useful in the study of the relation between homology and homotopy of nonsimply connected spaces. We show that this category admits the structure of a closed model category, in the sense of Quillen; notions of fibration, cofibration, and weak equivalence are defined and shown to satisfy fundamental properties that the corresponding notions satisfy in the category of spaces. This enables one to develop a ``homotopy theory'' for pro-spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0356039-8
Keywords: Pro-space, pro-map, tower of spaces, model category, weak equivalence, fibration, cofibration
Article copyright: © Copyright 1975 American Mathematical Society