Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.map_eq_iff_postcomp

∀ {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] (L : CategoryTheory.Functor C D)
  (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasLeftCalculusOfFractions] {X Y : C} (f₁ f₂ : X ⟶ Y),
  L.map f₁ = L.map f₂ ↔
    ∃ Z s, ∃ (_ : W s), CategoryTheory.CategoryStruct.comp f₁ s = CategoryTheory.CategoryStruct.comp f₂ s

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.MorphismProperty.HasLeftCalculusOfFractions