Theorems · Theorem · category theory

CategoryTheory.Quiv.pathComposition_naturality

∀ {C : Type u} {D : Type u₁} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Category.{v₁, u₁} D]
  (F : CategoryTheory.Functor C D),
  (CategoryTheory.Cat.freeMap F.toPrefunctor).comp (CategoryTheory.pathComposition D) =
    (CategoryTheory.pathComposition C).comp F

Naturality of pathComposition, which defines a natural transformation Quiv.forget ⋙ Cat.free ⟶ 𝟭 _.

Defined in

Mathlib.CategoryTheory.Category.Quiv

Cited by

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Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category