Theorems · Definition · category theory

HomologicalComplex.natTransOpCyclesToCycles

(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) →
          (i j : ι) →
            [inst_2 : CategoryTheory.CategoryWithHomology C] →
              HomologicalComplex.opcyclesFunctor C c i ⟶ HomologicalComplex.cyclesFunctor C c j

The natural transformation K.opcyclesToCycles i j : K.opcycles i ⟶ K.cycles j for all K : HomologicalComplex C c.

Defined in

Mathlib.Algebra.Homology.HomologySequence

Cited by

2 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryWithHomology