Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.LeftFraction.map_eq_iff

∀ {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) [inst_2 : L.IsLocalization W] [W.HasLeftCalculusOfFractions] {X Y : C}
  (φ ψ : W.LeftFraction X Y), φ.map L ⋯ = ψ.map L ⋯ ↔ CategoryTheory.MorphismProperty.LeftFractionRel φ ψ

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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