Theorems · Theorem · category theory

imageToKernel_arrow_assoc

∀ {V : Type u} [inst : CategoryTheory.Category.{v, u} V] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {A B C : V}
  (f : A ⟶ B) [inst_2 : CategoryTheory.Limits.HasImage f] (g : B ⟶ C) [inst_3 : CategoryTheory.Limits.HasKernel g]
  (w : CategoryTheory.CategoryStruct.comp f g = 0) {Z : V} (h : B ⟶ Z),
  CategoryTheory.CategoryStruct.comp (imageToKernel f g w)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobject g).arrow h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.imageSubobject f).arrow h

Defined in

Mathlib.Algebra.Homology.ImageToKernel

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasImageCategoryTheory.Limits.HasKernel