Theorems · Definition · category theory

HomologicalComplex.cyclesMap

{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 L : HomologicalComplex C c} →
            (K ⟶ L) → (i : ι) → [inst_2 : K.HasHomology i] → [inst_3 : L.HasHomology i] → K.cycles i ⟶ L.cycles i

The map K.cycles i ⟶ L.cycles i induced by a morphism in HomologicalComplex.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

59 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology