In mathematics, polyad is a concept of
category theory introduced by
Jean Bénabou
Jean Bénabou (1932 – 11 February 2022) was a Moroccan-born French mathematician, known for his contributions to category theory.
He directed the Research Seminar in Category Theory at the Institut Henri Poincaré and Institut de mathémati ...
in generalising
monad
Monad may refer to:
Philosophy
* Monad (philosophy), a term meaning "unit"
**Monism, the concept of "one essence" in the metaphysical and theological theory
** Monad (Gnosticism), the most primal aspect of God in Gnosticism
* ''Great Monad'', an ...
s.
A polyad in a
bicategory
In mathematics, a bicategory (or a weak 2-category) is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not (strictly) associative, but only associative ''up to'' an isom ...
''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.
Notes
Bibliography
*
Category theory
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