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
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.
The category of comodules
Let be a commutative ring and let . Then one has the following properties:
Properties of the category of comodules over a coalgebra are studied in
- Manfred Wischnewsky?, On linear representations of affine groups, I, Pacific Journal of Mathematics, Vol. 61, No. 2, 1975, Project Euclid.
Revised on June 25, 2014 12:13:10
by Adeel Khan