Theorems · Definition · category theory

CategoryTheory.Abelian.FunctorCategory.imageObjIso

{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.image α).obj X ≅ CategoryTheory.Abelian.image (α.app X)

The abelian image in a functor category can be calculated componentwise.

Defined in

Mathlib.CategoryTheory.Abelian.FunctorCategory

Cited by

4 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian