 Comodule

A right comodule is an object $M$ with a coaction $\rho :M\to M\otimes C$ satisfying the coassociativity and counit laws. This definition extends from coalgebras to comonoids in a monoidal category.

A comodule is a concept from category theory and algebra, specifically in the context of module theory and representation theory. In simple terms, a comodule can be thought of as a structure that is dual to a module over a coalgebra in a manner analogous to how modules relate to algebras.