Theorems · Theorem · category theory

CategoryTheory.Localization.liftNatTrans_add

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
  [inst_4 : CategoryTheory.Preadditive E] (F₁ F₂ : CategoryTheory.Functor C E) (F₁' F₂' : CategoryTheory.Functor D E)
  [inst_5 : CategoryTheory.Localization.Lifting L W F₁ F₁'] [inst_6 : CategoryTheory.Localization.Lifting L W F₂ F₂']
  (τ τ' : F₁ ⟶ F₂),
  CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' (τ + τ') =
    CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' τ +
      CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' τ'

Defined in

Mathlib.CategoryTheory.Localization.Preadditive

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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