Theorems · Theorem · category theory

CategoryTheory.Bicategory.LeftLift.IsKan.hom_ext

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b c : B} {f : b ⟶ a} {g : c ⟶ a}
  {t : CategoryTheory.Bicategory.LeftLift f g} (H : t.IsKan) {k : c ⟶ b} {τ τ' : t.lift ⟶ k},
  CategoryTheory.CategoryStruct.comp t.unit (CategoryTheory.Bicategory.whiskerRight τ f) =
      CategoryTheory.CategoryStruct.comp t.unit (CategoryTheory.Bicategory.whiskerRight τ' f) →
    τ = τ'

Two 2-morphisms out of a left Kan lift are equal if their compositions with each triangle 2-morphism are equal.

Defined in

Mathlib.CategoryTheory.Bicategory.Kan.IsKan

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory