Theorems · Definition · category theory

CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        (F : CategoryTheory.StrictlyUnitaryLaxFunctor B C) →
          (x : B) → CategoryTheory.CategoryStruct.id (F.obj x) ≅ F.map (CategoryTheory.CategoryStruct.id x)

Promote the morphism F.mapId x : 𝟙 (F.obj x) ⟶ F.map (𝟙 x) to an isomorphism when F is strictly unitary.

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary

Cited by

2 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory