Comodule

Summary

A comodule over a coalgebra $C$ is a vector space $M$ with a coaction $\rho \colon M \to M \otimes C$, the dual notion of a module over an algebra. Comodules over the coordinate ring of an affine algebraic group are the same as its rational representations. Comodules over the group algebra $KG$ with its standard coalgebra structure are the same as $G$-graded vector spaces. Comodules are as basic for coalgebras and Hopf algebras as modules are for rings.