Theorems · Definition · category theory

HomologicalComplex.toCycles

{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 j : ι) → [inst_2 : K.HasHomology j] → K.X i ⟶ K.cycles j

The map K.X i ⟶ K.cycles j induced by the differential K.d i j.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

19 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology