Theorems · Theorem · category theory

imageToKernel_zero_right

∀ {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.HasImages V] {w : CategoryTheory.CategoryStruct.comp f 0 = 0},
  imageToKernel f 0 w =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.imageSubobject f).arrow
      (CategoryTheory.inv (CategoryTheory.Limits.kernelSubobject 0).arrow)

Defined in

Mathlib.Algebra.Homology.ImageToKernel

Cited by

0 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasImages