Theorems · Definition · category theory

CochainComplex.HomComplex.Cocycle.toSingleMk

{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 : ℤ} →
              (f : K.X p ⟶ X) →
                {n : ℤ} →
                  p + n = q →
                    (p' : ℤ) →
                      p' + 1 = p →
                        CategoryTheory.CategoryStruct.comp (K.d p' p) f = 0 →
                          CochainComplex.HomComplex.Cocycle K ((CochainComplex.singleFunctor C q).obj X) n

Constructor for cocycles to a single complex.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

19 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject