Catégories dérivables

Denis-Charles Cisinski (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

This paper is devoted to the construction of derivators from a notion of model category which is general enough to recover the theories of Quillen, Thomason, and Brown. We develop, in particular, the theory of derivable exact categories (for instance, Frobenius categories or complicial biWaldhausen categories with nice homotopy stability properties), which give rise to triangulated derivators. At last, we prove that the notion of model category we introduced here is stable by taking presheaves categories over an arbitrary small category.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Denis-Charles Cisinski. Catégories dérivables. Bulletin de la société mathématique de France, 2010, 138 (3), pp.317-393. ⟨hal-00440930v2⟩