Theorems · Definition · category theory

CochainComplex.HomComplex.CohomologyClass.homAddEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {K L : CochainComplex C ℤ} →
        {n : ℤ} →
          CochainComplex.HomComplex.CohomologyClass K L n ≃+
            ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K ⟶
              (HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj
                ((CategoryTheory.shiftFunctor (HomologicalComplex C (ComplexShape.up ℤ)) n).obj L))

Cohomology classes identify to morphisms in the homotopy category.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive