We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax monoidal functors is investigated. We introduce tensor product of representations of bimonoids as a functorial binary operation and show how symmetric lax monoidal functors act on this product. Finally we apply the general theory to classical and quantum… Expand

La categorie des algebres quadratiques est munie d'une structure tensorielle. Ceci permet de construire des algebres de Hopf du type «(semi)-groupes quantiques»

The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of… Expand

We construct Quantum Representation Theory which describes quantum analogue of representations in frame of"non-commutative linear geometry"developed by Manin. To do it we generalise the internal… Expand