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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homotopy theories for diagrams of spaces


Author: E. Dror Farjoun
Journal: Proc. Amer. Math. Soc. 101 (1987), 181-189
MSC: Primary 55P91; Secondary 18G30, 55N91, 55P10, 55T15
MathSciNet review: 897092
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Abstract: We show that the category of diagrams of topological spaces (or simplicial sets) admits many interesting model category structures in the sense of Quillen [8]. The strongest one renders any diagram of simplicial complexes and simplicial maps between them both fibrant and cofibrant. Namely, homotopy invertible maps between such are the weak equivalences and they are detectable by the "spaces of fixed points." We use a generalization of the method for defining model category structure of simplicial category given in [5].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0897092-6
PII: S 0002-9939(1987)0897092-6
Keywords: Diagrams of spaces, model category, singular functors, equivariant homotopy theory
Article copyright: © Copyright 1987 American Mathematical Society