REACTION OF BRAID-GROUPS WITH A CATEGORY

We describe how to define by generators and relations an action of the braid group on a category. More generally, how to define a functor fr om a generalized positive braids monoid, corresponding to a finite Cox eter group, to a monoidal category. Applications to constructions of B ondal (exceptional systems) and of Broue-Michel (correspondences on fl ag manifolds) are given.