Polyad (mathematics)

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 : C → 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 Φ : C → D where C has only one object.

Notes

^ Benabou, Jean (1967), "Introduction to Bicategories", Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, vol. 47, pp. 1–77, doi:10.1007/BFb0074299, ISBN 978-3-540-03918-1

Bibliography

Street, Ross (1983), "Enriched Categories and Cohomology", Quaestiones Mathematicae, 6 (1–3): 265–283, doi:10.1080/16073606.1983.9632304
- Street, Ross (2005) [1983], "Enriched categories and cohomology" (PDF), Reprints in Theory and Applications of Categories, 14: 1–18
Leinster, Tom (1999). "Generalized Enrichment for Categories and Multicategories". arXiv:math/9901139.
Garner, Richard; Shulman, Michael (2016). "Enriched categories as a free cocompletion". Advances in Mathematics. 289: 1–94. doi:10.1016/j.aim.2015.11.012.

[1] Benabou, Jean (1967), "Introduction to Bicategories", Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, vol. 47, pp. 1–77, doi:10.1007/BFb0074299, ISBN 978-3-540-03918-1

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