Algebras and modules
Model category presentations
Geometry on formal duals of algebras
A comodule is to a comonoid as a module is to a monoid. Where a module is equipped with an action, a comodule is dually equipped with a coaction.
Given a comonoid with comultiplication and counit in a monoidal category , and an object in , a left -coaction is
coassociative i.e. (for nonstrict use the canonical isomorphism to compare the sides)
and counital i.e. (in this formula, is identified with ).
In some monoidal categories, e.g. of (super)vector spaces, and of Hilbert spaces, one often says (left/right) corepresentation instead of (left/right) coaction.
Revised on November 15, 2013 06:15:09
by Urs Schreiber