Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.homologyIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} → (h : S.LeftHomologyData) → [inst_2 : S.HasHomology] → S.homology ≅ h.H

When a short complex has homology, its homology can be computed using any left homology data.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

34 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomology