Homotopy models and localisations
by
Luca Mauri
Universität Duisburg

Models for homotopy-like Quillen models-provide an abstract basis for representation theorems in homological algebra. We analyse these models from a purely category-theoretical viewpoint. In fact, given a category C and a suitable class of arrows in it, there is a general way of defining an unstable triangulated structure on the localisation. The construction uses derived functors to define homotopy pullbacks for the localisation. Homotopy pullbacks, in turn, are used to defined fibration sequences and unstable triangles. The way the various homotopy models enter in this picture is by providing existence theorems for the Kan extensions defining the derived functors involved in the construction, and as such they can be analysed abstractly.

Date received: May 31, 2002