When does an endofunctor derive from an adjunction?

Theory Lunch

This is the first of two talks based on Andrea Schalk’s very good introduction to monads, which can be retrieved HERE

In the following, if $latex mathcal{C}$ is a category, we indicate by $latex |mathcal{C}|$ the collection of objects of $latex mathcal{C}$, and by $latex mathcal{C}(A,B)$ the collection of morphisms in $latex mathcal{C}$ from $latex A$ to $latex B$.

As we know, there are two basic ways of defining an adjunction:

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