nLab
mixed model structure

Definition

Let MM be a category with two closed model structures (C q,W q,F q)(C_q,W_q,F_q) and (C h,W h,F h)(C_h,W_h,F_h), and assume that F hF qF_h\subseteq F_q and W hW qW_h \subseteq W_q.

Theorem

There is a (necessarily unique closed) mixed model structure (C m,W q,F h)(C_m,W_q,F_h) on MM in which the fibrations are the hh-fibrations, but the weak equivalences are the qq-equivalences.

Properties

An object is cofibrant in the mixed model structure if and only if it has the hh-homotopy type of a qq-cofibrant object.

Examples

References

The original paper is

  • Michael Cole?, Mixing model structures, Top. Appl. 153 (2006) 1016–1032

There is also an exposition in

Revised on May 27, 2012 03:27:16 by Tim Campion? (128.112.203.118)