Theorems · Definition · category theory

CategoryTheory.Bicategory.Lan.CommuteWith.lanCompIsoWhisker

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b c : B} →
      (f : a ⟶ b) →
        (g : a ⟶ c) →
          [inst_1 : CategoryTheory.Bicategory.HasLeftKanExtension f g] →
            {x : B} →
              (h : c ⟶ x) →
                [inst_2 : CategoryTheory.Bicategory.Lan.CommuteWith f g h] →
                  CategoryTheory.Bicategory.lanLeftExtension f (CategoryTheory.CategoryStruct.comp g h) ≅
                    (CategoryTheory.Bicategory.lanLeftExtension f g).whisker h

The isomorphism f⁺ (g ≫ h) ≅ f⁺ g ≫ h at the level of structured arrows.

Defined in

Mathlib.CategoryTheory.Bicategory.Kan.HasKan

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory.HasLeftKanExtensionCategoryTheory.Bicategory.Lan.CommuteWith