Homology, Homotopy and Applications

Volume 8 (2006)

Number 1

Codescent theory II: cofibrant approximations

Pages: 211 – 242

DOI: https://dx.doi.org/10.4310/HHA.2006.v8.n1.a7


Paul Balmer (Department of Mathematics, ETH Zentrum, Zürich, Switzerland)

Michel Matthey (IGAT, EPFL, University of Lausanne, Switzerland)


We establish a general method to produce cofibrant approximations in the model category $U_S(C,D)$ of $S$-valued $C$-indexed diagrams with $D$-weak equivalences and $D$-fibrations. We also present explicit examples of such approximations. Here, $S$ is an arbitrary cofibrantly generated simplicial model category, and $D ⊂ C$ are small categories. An application to the notion of homotopy colimit is presented.


diagram category, cofibrant approximation, codescent

2010 Mathematics Subject Classification

Primary 18G55. Secondary 55U10.

Published 1 January 2006