Theorems · Theorem · category theory

CategoryTheory.Localization.liftNatTrans_app

∀ {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_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  [inst_3 : L.IsLocalization W] (F₁ F₂ : CategoryTheory.Functor C E) (F₁' F₂' : CategoryTheory.Functor D E)
  [inst_4 : CategoryTheory.Localization.Lifting L W F₁ F₁'] [inst_5 : CategoryTheory.Localization.Lifting L W F₂ F₂']
  (τ : F₁ ⟶ F₂) (X : C),
  (CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' τ).app (L.obj X) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Localization.Lifting.iso L W F₁ F₁').hom.app X)
      (CategoryTheory.CategoryStruct.comp (τ.app X) ((CategoryTheory.Localization.Lifting.iso L W F₂ F₂').inv.app X))

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

20 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Localization.LiftingCategoryTheory.Localization.Lifting