The notion of a comonadic functor is the dual of that of a monadic functor. See there for more background.
Given a pair of adjoint functors, , with counit and unit , one forms a comonad by , . comodules form a category and there is a natural comparison functor given by .
A functor is comonadic if it has a right adjoint and the corresponding comparison functor is an equivalence of categories. The adjunction is said to be a comonadic adjunction.
Beck’s monadicity theorem has its dual, comonadic analogue. To discuss it, observe that for every -comodule ,
manifestly exhibits a split equalizer sequence.
Revised on May 18, 2011 15:33:18
by Urs Schreiber