Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_eq_map

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {W : CategoryTheory.MorphismProperty C}
  [inst_2 : W.HasLeftCalculusOfFractions] {X Y Z : C} (z₁ : W.LeftFraction X Y) (z₂ : W.LeftFraction Y Z)
  (z₃ : W.LeftFraction z₁.Y' z₂.Y'),
  CategoryTheory.CategoryStruct.comp z₂.f z₃.s = CategoryTheory.CategoryStruct.comp z₁.s z₃.f →
    ∀ (L : CategoryTheory.Functor C D) [inst_3 : L.IsLocalization W],
      CategoryTheory.CategoryStruct.comp (z₁.map L ⋯) (z₂.map L ⋯) = (z₁.comp₀ z₂ z₃).map L ⋯

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

2 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.HasLeftCalculusOfFractionsCategoryTheory.Functor.IsLocalization