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.
strictly preserves identity objects and they commute with horizontal composition in C and D. See [3] for more details and for lax versions.
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