Theorems · Theorem · category theory

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