Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.FunctorialFactorizationData.i_mapZ

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) {X Y X' Y' : C} {f : X ⟶ Y} {g : X' ⟶ Y'}
  (φ : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk g),
  CategoryTheory.CategoryStruct.comp (data.factorizationData f).i (data.mapZ φ) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Arrow.Hom.left φ) (data.factorizationData g).i

Defined in

Mathlib.CategoryTheory.MorphismProperty.Factorization

Cited by

1 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category