Abstract: This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras for a monad, comonads and coalgebras, and algebras for endofunctors. Exercises are given in the last part of the chapter.

Keywords: adjunctions, triangle identities, monads, adjoints, comonads, algebras, endofunctors,