Girish Mahajan (Editor)

Lax natural transformation

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In the mathematical field of category theory, specifically the theory of 2-categories, a lax natural transformation is a kind of morphism between 2-functors.

Definition

Let C and D be 2-categories, and let F , G : C → D be 2-functors. A lax natural transformation α : F → G between them consists of

  • a morphism α c : F ( c ) → G ( c ) in D for every object c ∈ C and
  • a 2-morphism α f : G ( f ) ∘ α c → α c ′ ∘ F ( f ) for every morphism f : c → c ′ in C

    • satisfying some equations (see or )

    References

    Lax natural transformation Wikipedia
    (Text) CC BY-SA