Theorems · Theorem · category theory

CategoryTheory.Localization.isoOfHom_inv_hom_id

∀ {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] {X Y : C} (f : X ⟶ Y) (hf : W f),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.isoOfHom L W f hf).inv (L.map f) =
    CategoryTheory.CategoryStruct.id (L.obj Y)

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

5 results in Mathlib

Foundations

Depth 12 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization