algebra for an endomorphism
If is a bicategory and is an endomorphism in , then a (left) -algebra or -module is given by a 1-cell together with a 2-cell .
One can also define right modules/algebras, comodules/coalgebras and bimodules as for monads.
If is , an algebra for an endofunctor is the same thing as an -algebra in the sense above.
Every module over a monad is an algebra over the underlying endomorphism .
An algebra for a profunctor (q.v.) on is essentially the same as a -coalgebra in , the bicategory of categories and profunctors.
Revised on September 23, 2010 21:13:48
by Finn Lawler