Theorems · Theorem · category theory

CategoryTheory.Abelian.coimage_image_factorisation_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {P Q : C}
  (f : P ⟶ Q) [inst_2 : CategoryTheory.Limits.HasCokernel f] [inst_3 : CategoryTheory.Limits.HasKernel f]
  [inst_4 : CategoryTheory.Limits.HasKernel (CategoryTheory.Limits.cokernel.π f)]
  [inst_5 : CategoryTheory.Limits.HasCokernel (CategoryTheory.Limits.kernel.ι f)] {Z : C} (h : Q ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.coimage.π f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.coimageImageComparison f)
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.image.ι f) h)) =
    CategoryTheory.CategoryStruct.comp f h

Defined in

Mathlib.CategoryTheory.Abelian.Images

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasCokernelCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasCokernel