Theorems · Theorem · algebraic topology

SSet.fromNormalizedChainComplex_f_toNormalizedChainComplex_f

∀ {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 : ℕ),
  CategoryTheory.CategoryStruct.comp ((X.fromNormalizedChainComplex R).f n) ((X.toNormalizedChainComplex R).f n) =
    CategoryTheory.CategoryStruct.id ((X.normalizedChainComplex R).X n)

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 1 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive

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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
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
HomologicalComplex.Xstatement and proof · cited by 1,839
SSetstatement and proof · cited by 1,283
HomologicalComplex.Hom.fstatement and proof · cited by 845
ComplexShape.downstatement · cited by 605
CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
SSet.chainComplexstatement · cited by 46
SSet.normalizedChainComplexstatement and proof · cited by 29

Cited by1

Results whose statement or proof uses this declaration.

SSet.fromNormalizedChainComplex_f_toNormalizedChainComplex_f_assocproof · cited by 0