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Weak Factorizations, Fractions and Homotopies

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Abstract

We show that the homotopy category can be assigned to any category equipped with a weak factorization system. A classical example of this construction is the stable category of modules. We discuss a connection with the open map approach to bisimulations proposed by Joyal, Nielsen and Winskel.

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Authors and Affiliations

  1. Department of Computer Science, University of Leicester, Leicester, LE1 7RH, UK

    Alexander Kurz

  2. Department of Algebra and Geometry, Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    JiřÍ Rosický

Authors
  1. Alexander Kurz
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  2. JiřÍ Rosický
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Additional information

Mathematics Subject Classifications (2000)

18A99, 55P10, 68Q85.

JiřÍ Rosický: Supported by the Grant Agency of the Czech Republic under the grant 201/02/0148.

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Kurz, A., Rosický, J. Weak Factorizations, Fractions and Homotopies. Appl Categor Struct 13, 141–160 (2005). https://doi.org/10.1007/s10485-004-6730-z

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  • DOI: https://doi.org/10.1007/s10485-004-6730-z

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