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In mathematics, polyad is a concept of category theory introduced by Jean Bénabou in generalising monads.[1] A polyad in a bicategory D is a bicategory morphism Φ from a locally punctual bicategory C to D, Φ : CD. (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 Φ : CD where C has only one object.


  1. ^ Benabou, Jean (1967), Introduction to Bicategories 


  • Street, Ross (1983), Enriched Categories and Cohomology