Theorems · Theorem · category theory

CategoryTheory.FreeGroupoid.mapCompLift_hom_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₁} [inst_1 : CategoryTheory.Category.{v₁, u₁} D]
  {E : Type u₂} [inst_2 : CategoryTheory.Groupoid E] (F : CategoryTheory.Functor C D) (G : CategoryTheory.Functor D E)
  (X : CategoryTheory.FreeGroupoid C),
  (CategoryTheory.FreeGroupoid.mapCompLift F G).hom.app X =
    CategoryTheory.CategoryStruct.id
      (((CategoryTheory.FreeGroupoid.map F).comp (CategoryTheory.FreeGroupoid.lift G)).obj X)

Defined in

Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Groupoid