Mathematical Proceedings of the Cambridge Philosophical Society

Sheafifiable homotopy model categories

a1 Mathematical Institute, Utrecht University, Utrecht, The Netherlands; e-mail:


If a Quillen model category can be specified using a certain logical syntax (intuitively, ‘is algebraic/combinatorial enough’), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric morphisms to Quillen model categories and Quillen adjunctions.

(Received June 3 1999)
(Revised September 17 1999)