Semi-direct product of categories and twisted actions of categorical groups
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
A (strict) categorical group is a (strict) monoidal category with an additional operation of 'inversion' under monoidal product. It has an equivalent description in terms of crossed modules. In order to study the representations/actions of categorical groups, we introduce a notion of semi-direct product of categories. It turns out that there are many interesting examples of semi-direct product of categories. In particular I will give some examples where one of the category is a (strict) categorical group. We use the notion of semi direct product of categories to define a kind of 'twisted action' of a categorical group. If time permits I will discuss a version of Schur's lemma in this context.
Reference:Twisted actions of categorical groups, S Chatterjee, A Lahiri, A Sengupta, Theory and Applications of Categories, Vol. 29, 2014, No. 8, pp 215-255