Theorems · Theorem · category theory

CochainComplex.exists_iso_single

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : CochainComplex C ℤ) [inst_2 : CategoryTheory.Limits.HasZeroObject C] (n : ℤ) [K.IsStrictlyGE n]
  [K.IsStrictlyLE n], ∃ M, Nonempty (K ≅ (HomologicalComplex.single C (ComplexShape.up ℤ) n).obj M)

A cochain complex that is both strictly ≤ n and ≥ n is isomorphic to a complex (single _ _ n).obj M for some object M.

Defined in

Mathlib.Algebra.Homology.Embedding.CochainComplex

Cited by

1 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCochainComplex.IsStrictlyGECochainComplex.IsStrictlyLE