Theorems · Definition · category theory

CochainComplex.HomComplex.Cochain.toSingleEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        {X : C} →
          {K : CochainComplex C ℤ} →
            {p q n : ℤ} →
              p + n = q →
                CochainComplex.HomComplex.Cochain K ((CochainComplex.singleFunctor C q).obj X) n ≃+ (K.X p ⟶ X)

Cochains of degree n from (singleFunctor C q).obj X to K identify to K.X p ⟶ X when p + n = q.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

11 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject