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
-
^ Kelly, G.M.; Street, R. (1974). "Review of the elements of 2-categories". Category Seminar. 420: 75–103.
-
^ G. M. Kelly. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories, (10), 2005.
-
^
2-functor at the
nLab