Theorems · Theorem · category theory

CategoryTheory.Localization.exists_leftFraction

∀ {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}
  (f : L.obj X ⟶ L.obj Y), ∃ φ, f = φ.map L ⋯

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions

Cited by

14 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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