The first axiom is akin to the associativity in monoids if we think of formula_29 as the monoid's binary operation, and the second axiom is akin to the existence of an identity element (which we think of as given by formula_30). Indeed, a monad on formula_9 can alternatively be defined as a monoid in the category formula_32 whose objects are the endofunctors of formula_9 and whose morphisms are the natural transformations between them, with the monoidal structure induced by the composition of endofunctors.