Theorems · Theorem · category theory

CategoryTheory.Localization.comp_liftNatTrans_assoc

∀ {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 F₃ : CategoryTheory.Functor C E) (F₁' F₂' F₃' : CategoryTheory.Functor D E)
  [h₁ : CategoryTheory.Localization.Lifting L W F₁ F₁'] [h₂ : CategoryTheory.Localization.Lifting L W F₂ F₂']
  [h₃ : CategoryTheory.Localization.Lifting L W F₃ F₃'] (τ : F₁ ⟶ F₂) (τ' : F₂ ⟶ F₃) {Z : CategoryTheory.Functor D E}
  (h : F₃' ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' τ)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.liftNatTrans L W F₂ F₃ F₂' F₃' τ') h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Localization.liftNatTrans L W F₁ F₃ F₁' F₃' (CategoryTheory.CategoryStruct.comp τ τ')) h

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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