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Some videos introducting adjunctions and their relationship to monads.
The notion of an adjunction. Definition via unit and counit natural transformations and the triangle identities.
Definition of adjunction via natural isomorphism between hom-sets. Getting the unit and counit from this.
Adjunctions give rise to monads.
The two notions of adjunction coincide.
Every monad comes from an adjunction via its category of algebras.
Definition of the Kleisli category
The adjunction coming from the Kleisli category. The category of adjunctions for a monad: the Eilenberg-Moore and Kleisli categories as terminal and initial objects.