nLab
comonoid

A comonoid (or comonoid object) in a monoidal category MM is a monoid object in the opposite category M opM^{op} (which is a monoidal category using the same operation as in MM).

For example, a comonoid in Vect (with its usual tensor product) is called a coalgebra. Every set can be made into a comonoid in Set (with the cartesian product) in a unique way. More generally, every object in a cartesian monoidal category can be made into a comonoid in a unique way.

Revised on September 5, 2010 21:58:09 by Toby Bartels (75.117.105.28)