Theorems · Theorem · category theory

CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type w} [inst_1 : CategoryTheory.Category.{z, w} D]
  [inst_2 : CategoryTheory.Abelian D] {F G : CategoryTheory.Functor C D} (α : F ⟶ G) (X : C),
  CategoryTheory.Abelian.coimageImageComparison (α.app X) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.FunctorCategory.coimageObjIso α X).inv
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.Abelian.coimageImageComparison α).app X)
        (CategoryTheory.Abelian.FunctorCategory.imageObjIso α X).hom)

Defined in

Mathlib.CategoryTheory.Abelian.FunctorCategory

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian