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2-functor

From Wikipedia, the free encyclopedia

In mathematics, specifically, in category theory, a 2-functor is a morphism between 2-categories.[1] They may be defined formally using enrichment by saying that a 2-category is exactly a Cat-enriched category and a 2-functor is a Cat-functor.[2]

Explicitly, if C and D are 2-categories then a 2-functor consists of

  • a function , and
  • for each pair of objects , a functor

such that each strictly preserves identity objects and they commute with horizontal composition in C and D.

See [3] for more details and for lax versions.

References

[edit]
  1. ^ Kelly, G. M.; Street, Ross (1974). "Review of the elements of 2-categories". In Kelly, Gregory M. (ed.). Category Seminar: Proceedings of the Sydney Category Theory Seminar, 1972/1973. Lecture Notes in Mathematics. Vol. 420. Springer. pp. 75–103. doi:10.1007/BFb0063101. ISBN 978-3-540-06966-9. MR 0357542.
  2. ^ G. M. Kelly. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories, (10), 2005.
  3. ^ 2-functor at the nLab