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In mathematics, 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.