nLab coalgebra over a comonad




A coalgebra or comodule over a comonad CC on a category AA is an object aAa\in A with a morphisms aCaa\to C a satisfying axioms formally dual to those for an algebra over a monad. The category of coalgebras is called its (co-)Eilenberg-Moore category and satisfies a universal property dual to that of the Eilenberg-Moore object for a monad; it can thereby be internalized to any 2-category. The forgetful functor from the category of coalgebras to the category AA is called a comonadic functor. Similarly, a comonad also has a co-Kleisli category.


Some introductory material on comonads, coalgebras and co-Kleisli morphisms can be found in

  • Paolo Perrone, Notes on Category Theory with examples from basic mathematics, Chapter 5. (arXiv)

On model category-structures on coalgebras over a comonad:

Last revised on August 17, 2022 at 11:12:33. See the history of this page for a list of all contributions to it.