Theorems · Theorem · algebraic topology

SSet.isZero_homology_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) [inst_3 : CategoryTheory.CategoryWithHomology C] (n d : ℕ)
  [X.HasDimensionLT d],
  autoParam (d ≤ n) SSet.isZero_homology_of_hasDimensionLT._auto_1 → CategoryTheory.Limits.IsZero (X.homology R n)

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 0 results in Mathlib
Foundations: Depth 110 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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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SSetstatement and proof · cited by 1,283
CategoryTheory.Limits.IsZerostatement · cited by 306
CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
SSet.chainComplexproof · cited by 46
SSet.HasDimensionLTstatement and proof · cited by 32
HomologicalComplex.exactAt_iff_isZero_homologyproof · cited by 13
SSet.homologystatement · cited by 13
SSet.exactAt_chainComplex_of_hasDimensionLTproof · cited by 1

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