Annulé - Representations of categorical groups and semi-direct product of categories - Annulé

A categorical group is a monoidal category with associator, left-right unitor are identity. Thus under the tensor product, both object and morphism sets are groups. Categorical groups have an equivalent description in terms of "crossed-modules". We will discuss the representations of categorical groups on "certain categorical spaces" and some of the consequences. We will introduce the notion of semi-direct product of categories and show how this notion can be used to give a more general description of representations of categorical groups. This is a joint work with A. Lahiri, A. N. Sengupta.