Theorems · Theorem · category theory

imageToKernel_comp_left

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

Defined in

Mathlib.Algebra.Homology.ImageToKernel

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelsCategoryTheory.Limits.HasImages