Theorems · Definition · category theory

HomologicalComplex.opcyclesToCycles

{C : Type u_1} →
  {ι : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {c : ComplexShape ι} →
          (K : HomologicalComplex C c) →
            (i j : ι) → [inst_2 : K.HasHomology i] → [inst_3 : K.HasHomology j] → K.opcycles i ⟶ K.cycles j

The morphism K.opcycles i ⟶ K.cycles j that is induced by K.d i j.

Defined in

Mathlib.Algebra.Homology.HomologySequence

Cited by

18 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology