Série de Courts Exposés

Semi-direct product of categories and twisted actions of categorical groups

by Prof. Saikat CHATTERJEE (IHÉS)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
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