Theorems · Definition · category theory

CategoryTheory.FreeGroupoid.homRel.recOn

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {motive : ⦃X Y : Quiver.FreeGroupoid C⦄ → (a a_1 : X ⟶ Y) → CategoryTheory.FreeGroupoid.homRel C a a_1 → Prop}
  ⦃X Y : Quiver.FreeGroupoid C⦄ {a a_1 : X ⟶ Y} (t : CategoryTheory.FreeGroupoid.homRel C a a_1),
  (∀ (X : C),
      motive ((Quiver.FreeGroupoid.of C).map (CategoryTheory.CategoryStruct.id X))
        (CategoryTheory.CategoryStruct.id ((Quiver.FreeGroupoid.of C).obj X)) ⋯) →
    (∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z),
        motive ((Quiver.FreeGroupoid.of C).map (CategoryTheory.CategoryStruct.comp f g))
          (CategoryTheory.CategoryStruct.comp ((Quiver.FreeGroupoid.of C).map f) ((Quiver.FreeGroupoid.of C).map g))
          ⋯) →
      motive a a_1 t

Defined in

Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category