Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.LeftFraction.map_eq_of_map_eq

∀ {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} {X Y : C}
  (φ₁ φ₂ : W.LeftFraction X Y) {E : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  (L₁ : CategoryTheory.Functor C D) (L₂ : CategoryTheory.Functor C E) [inst_3 : L₁.IsLocalization W]
  [inst_4 : L₂.IsLocalization W], φ₁.map L₁ ⋯ = φ₂.map L₁ ⋯ → φ₁.map L₂ ⋯ = φ₂.map L₂ ⋯

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLocalization