Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyData.canonical

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

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

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

10 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomology