In mathematics, polyad is a concept of category theory

Category theory

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...

 introduced by Jean Bénabou in generalising monad

Monad (category theory)

In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an functor, together with two natural transformations...

s. A polyad in a bicategory

Bicategory

In mathematics, a bicategory is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not associative, but only associative up to an isomorphism. The notion was introduced in 1967 by Jean Bénabou.Formally, a bicategory B...

D is a bicategory morphism Φ from a locally punctual bicategory C to D, . (A bicategory C is called locally punctual if all hom-categories C(X,Y) consist of one object and one morphism only.) Monads are polyads where C has only one object.