Theorems · Theorem · algebraic topology

SSet.isZero_normalizedChainComplex_X_of_hasDimensionLT

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasCoproducts C]
  [inst_2 : CategoryTheory.Preadditive C] (X : SSet) (R : C) (n d : ℕ) [X.HasDimensionLT d],
  autoParam (d ≤ n) SSet.isZero_normalizedChainComplex_X_of_hasDimensionLT._auto_1 →
    CategoryTheory.Limits.IsZero ((X.normalizedChainComplex R).X n)

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive SSet.HasDimensionLT

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Preadditivestatement and proof · cited by 3,309
HomologicalComplex.Xstatement and proof · cited by 1,839
SSetstatement and proof · cited by 1,283
ComplexShape.downstatement · cited by 605
CategoryTheory.Limits.IsZerostatement · cited by 306
LE.le.not_gtproof · cited by 189
CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
SSet.nonDegenerateproof · cited by 106
CategoryTheory.Limits.IsZero.iff_id_eq_zeroproof · cited by 40
SSet.HasDimensionLTstatement and proof · cited by 32

Cited by1

Results whose statement or proof uses this declaration.

SSet.exactAt_chainComplex_of_hasDimensionLTproof · cited by 1