Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.canonical

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

Given a short complex S such that S.HasHomology, this is the canonical left homology data for S whose K and H fields are respectively S.cycles and S.homology.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

7 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomology