Theorems · Theorem · category theory

imageToKernel_zero_left

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

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.HasZeroObject