The Eilenberg-Moore Category
An adjunction between two categories is a way of 'comparing' the two categories by means of two functors.
An adjunction always leaves some kind of structure on a category, called a monad. In this talk, we focus on trying to find a converse to the statement 'every adjunction gives rise to a monad': suppose you find some monad lying around somewhere, but you can't remember what adjunction that monad ever came from. Is it possible to construct an adjunction which gives rise to this monad?
One of the possible solutions to this question is the Eilenberg-Moore category, which we will investigate in this talk. We'll also consider the position of this solution in the category of all possible adjunctions giving rise to a given monad.