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Daniel Dugger and Brooke Shipley give an example in their paper A curious example of triangulated-equivalent model categories which are not Quillen equivalent available here.

Let us view topological K-theory as a functor $K$ from the cateory of compact pairs (that is, a compact Hausdorff spaces with a distinguished closed subset) to the category of $\mathbb Z/2$-graded Abe …

Consider six countable Abelian groups and six group homomorphims as in the following diagram G → H → I ↑ ↓ L ← K ← J Assume that the resulting sequence is exact at all six entries. Question …

I'm trying to follow an argument in Lück's "Algebraische Topologie: Homologie und Mannigfaltigkeiten" (to which there apparently doesn't exist an english translation). The aim is to check homotopy inv …

A general treatment of the Adams spectral sequence in the context of triangulated categories based on the work of Brinkmann and Christensen can be found here: http://arxiv.org/pdf/0801.1344. No monoi …

It is shown in Remark 7.1.12 of (a newer version of) Mark Hovey's book Model Categories that, in a stable model category, homotopy pullback squares coincide with homotopy pushout squares. The argument …

By a result of Schochet, the category of C*-algebras with homotopy equivalences and "Schochet fibrations" is a pointed category of fibrant objects whose homotopy category is the ordinary homotopy cate …