Theorems · Definition · category theory

CategoryTheory.FreeGroupoid.mapComp

{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.Category.{v₂, u₂} E] →
            (φ : CategoryTheory.Functor C D) →
              (φ' : CategoryTheory.Functor D E) →
                CategoryTheory.FreeGroupoid.map (φ.comp φ') ≅
                  (CategoryTheory.FreeGroupoid.map φ).comp (CategoryTheory.FreeGroupoid.map φ')

The functor induced by a composition is the composition of the functors they induce.

Defined in

Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category