Hopf monads on categories

Robert Wisbauer – 31 October 2007

Generalising modules over associative rings, the notion of modules for an endofunctor of any category is well established and useful in large parts of mathematics including universal algebra. Similarly, comodules over coalgebras are the model for comodules for an endofunctor and they are of basic importance. Compatibility conditions between endofunctors can be described by distributive laws. We use these ingredients to define (mixed) bimonads and Hopf monads on arbitrary categories thus making these notions accessible to universal algebra.