Theorems · Theorem · category theory

CategoryTheory.Localization.morphismProperty_eq_top

∀ {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] (P : CategoryTheory.MorphismProperty D)
  [P.RespectsIso] [P.IsMultiplicative],
  (∀ ⦃X Y : C⦄ (f : X ⟶ Y), P (L.map f)) →
    (∀ ⦃X Y : C⦄ (f : X ⟶ Y) (hf : W f), P (CategoryTheory.Localization.isoOfHom L W f hf).inv) → P = ⊤

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

1 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.IsMultiplicative