Theorems · Theorem · algebraic topology

SSet.exactAt_chainComplex_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) [CategoryTheory.CategoryWithHomology C] (n d : ℕ)
  [X.HasDimensionLT d],
  autoParam (d ≤ n) SSet.exactAt_chainComplex_of_hasDimensionLT._auto_1 →
    HomologicalComplex.ExactAt (X.chainComplex R) n

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 1 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive CategoryTheory.CategoryWithHomology SSet.HasDimensionLT

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Cites13

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.Preadditivestatement and proof · cited by 3,309
SSetstatement and proof · cited by 1,283
ComplexShape.downstatement · cited by 605
CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
SSet.chainComplexstatement · cited by 46
HomologicalComplex.ExactAtstatement · cited by 44
SSet.HasDimensionLTstatement and proof · cited by 32
SSet.toNormalizedChainComplexproof · cited by 20
exactAt_iff_of_quasiIsoAtproof · cited by 4
HomologicalComplex.ExactAt.of_isZeroproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

SSet.isZero_homology_of_hasDimensionLTproof · cited by 0