Rahul Sharma (Editor)

2 functor

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

In the mathematical field of Category theory, a 2-functor is a morphism between 2-categories. Because strict 2-categories can be defined as categories enriched in Cat, the category of small categories, a 2-functor can be defined succinctly as a Cat-enriched functor.

Spelling this out a bit, let C and D be 2-categories. A 2-functor F : C → D consists of

  • a function F : Ob C → Ob D , and
  • for each pair of objects c , c ′ ∈ C a functor F c , c ′ : Hom C ( c , c ′ ) → Hom D ( F c , F c ′ ) on hom-categories,

    • such that these functors strictly preserves identity objects and commute with compositions.

    See for more details and for lax versions.

    References

    2-functor Wikipedia
    (Text) CC BY-SA