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

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897092-6

MathSciNet review:
897092

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-1987-0897092-6

Keywords:
Diagrams of spaces,
model category,
singular functors,
equivariant homotopy theory

Article copyright:
© Copyright 1987
American Mathematical Society