Theorems · Definition · category theory

CochainComplex.HomComplex.Cocycle.fromSingleMk

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

Constructor for cocycles from a single complex.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

19 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject