commutes. Such a -algebra is also called an Eilenberg–Moore algebra. The forgetful functor from the category of Eilenberg–Moore algebras to has a left adjoint, exhibiting the monad as coming from a pair of adjoint functors (the Eilenberg–Moore construction).
See also Adjoint functor.
|[a1]||F. Borceux, "Handbook of categorical algebra: Categories and structures" , 2 , Cambridge Univ. Press (1994) pp. Chap. 4|
Eilenberg-Moore algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Eilenberg-Moore_algebra&oldid=17237