Theorems · Theorem · category theory

CategoryTheory.Localization.liftNatTrans_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) {E : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  [inst_3 : L.IsLocalization W] (F : CategoryTheory.Functor C E) (F' : CategoryTheory.Functor D E)
  [h : CategoryTheory.Localization.Lifting L W F F'],
  CategoryTheory.Localization.liftNatTrans L W F F F' F' (CategoryTheory.CategoryStruct.id F) =
    CategoryTheory.CategoryStruct.id F'

Defined in

Mathlib.CategoryTheory.Localization.Predicate

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.Localization.Lifting