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Closed model categories for the n-type of spaces and simplicial sets

Published online by Cambridge University Press:  24 October 2008

Carmen Elvira-Donazar  and
Luis-Javier Hernandez-Paricio
Carmen Elvira-Donazar
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Luis-Javier Hernandez-Paricio
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
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Abstract

For each integer n ≥ 0, we give a distinct closed model category structure to the categories of spaces and of simplicial sets. Recall that a non-empty map is said to be a weak equivalence if it induces isomorphisms on the homotopy groups for any choice of base point. Putting the condition on dimensions ≥ n, we have the notion of a weak n-equivalence which is at the base of the nth closed model category structure given here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 93 - 103
Copyright
Copyright © Cambridge Philosophical Society 1995

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