Frobenius functors between bicategories

John Bourke – 4 March 2009

Bicategories, lax functors, and lax transformations do not organize themselves int a good categorical structure, the reason being that one cannot whisker (on the right) a lax transformation along a lax functor. On the other hand one can whisker a lax transformation along a pseudofunctor. Between lax functors and pseudofunctors are (separable) Frobenius functors, which we shall see are also sufficient for such whiskering.