Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.map_eq_iff_precomp

∀ {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.HasRightCalculusOfFractions] {Y Z : C}
  (f₁ f₂ : Y ⟶ Z),
  L.map f₁ = L.map f₂ ↔
    ∃ X s, ∃ (_ : W s), CategoryTheory.CategoryStruct.comp s f₁ = CategoryTheory.CategoryStruct.comp s f₂

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

3 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.MorphismProperty.HasRightCalculusOfFractions