Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.ofAbelian

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] → (S : CategoryTheory.ShortComplex C) → S.LeftHomologyData

The canonical LeftHomologyData of a short complex S in an abelian category, for which the H field is Abelian.coimage (kernel.ι S.g ≫ cokernel.π S.f).

Defined in

Mathlib.Algebra.Homology.ShortComplex.Abelian

Cited by

4 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian