Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.toSingleMk_surjective

∀ {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} {q n : ℤ}
  (α : CochainComplex.HomComplex.Cocycle K ((CochainComplex.singleFunctor C q).obj X) n) (p : ℤ) (h : p + n = q)
  (p' : ℤ) (hp' : p' + 1 = p),
  ∃ f,
    ∃ (hf : CategoryTheory.CategoryStruct.comp (K.d p' p) f = 0),
      CochainComplex.HomComplex.Cocycle.toSingleMk f h p' hp' hf = α

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject