Theorems · Definition · category theory

CategoryTheory.Localization.qCompEquivalenceFromModelFunctorIso

{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.Q.comp (CategoryTheory.Localization.equivalenceFromModel L W).functor ≅ L

Via the equivalence of categories equivalenceFromModel L W : W.Localization ≌ D, one may identify the functors W.Q and L.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization