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On the homotopy type of classifying spaces

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Abstract

Let βC (resp. BC) be the Milnor (resp. Milgram) classifying space of a topological category C as defined by G. Segal [13]. We show that βC and BC are homotopy equivalent if the inclusion of the degenerate simplices into the space of all simplices is a cofibration.

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  1. Universität des Saarlandes Fachbereich 9 Mathematik, 66 Saarbrücken, Federal Republic of Germany

    Tammo tom Dieck

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  1. Tammo tom Dieck
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tom Dieck, T. On the homotopy type of classifying spaces. Manuscripta Math 11, 41–49 (1974). https://doi.org/10.1007/BF01189090

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  • DOI: https://doi.org/10.1007/BF01189090

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