Propriétés universelles et extensions de Kan dérivées, by Denis-Charles Cisinski

We show that for every small category A, the homotopy theory of presheaves of categories (or equivalently of simplicial sets) on A (i.e., the derivator associated to it) satisfies a universal property. We deduce a similar statement about the pointed version. The case of the final category allows us to define a canonical action of the derivator HOT (associated to the homotopy theory of spaces) on every right derivator. Hovey's homotopy coherence conjectures are consequences of these uniqueness results.

Denis-Charles Cisinski <>