Theorems · Theorem · category theory

CategoryTheory.Functor.essImage.liftFunctorCompIso_hom_app

∀ {J : Type u_1} {C : Type u_2} {D : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C] [inst_2 : CategoryTheory.Category.{v_3, u_3} D]
  (G : CategoryTheory.Functor J D) (F : CategoryTheory.Functor C D) [inst_3 : F.Full] [inst_4 : F.Faithful]
  (hG : ∀ (j : J), F.essImage (G.obj j)) (X : J),
  (CategoryTheory.Functor.essImage.liftFunctorCompIso G F hG).hom.app X =
    (F.toEssImage.objObjPreimageIso { obj := G.obj X, property := ⋯ }).hom.hom

Defined in

Mathlib.CategoryTheory.EssentialImage

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful