coalgebra over a comonad

A *coalgebra* or *comodule* over a comonad $C$ on a category $A$ is an object $a\in A$ with a morphisms $a\to C a$ 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 $A$ is called a comonadic functor. Similarly, a comonad also has a co-Kleisli category.

Created on March 31, 2016 at 05:06:37. See the history of this page for a list of all contributions to it.