Theorems · Definition · category theory

HomologicalComplex.cycles

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {ι : Type u_2} → {c : ComplexShape ι} → (K : HomologicalComplex C c) → (i : ι) → [K.HasHomology i] → C

The cycles in degree i of a homological complex.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

164 results in Mathlib

Foundations

Depth 25 from the axioms, rests on 144 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology