Theorems · Theorem · category theory

CategoryTheory.Functor.IsLocalization.of_equivalence_target

∀ {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) {E : Type u_4} [inst_2 : CategoryTheory.Category.{v_4, u_4} E]
  (L' : CategoryTheory.Functor C E) (eq : D ≌ E) [L.IsLocalization W] (e : L.comp eq.functor ≅ L'), L'.IsLocalization W

If L : C ⥤ D is a localization for W : MorphismProperty C, then it is also the case of a functor obtained by post-composing L with an equivalence of categories.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

8 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization