Theorems · Theorem · algebraic topology

SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_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.toNormalizedChainComplex R).f n) ((X.fromNormalizedChainComplex R).f n) =
    AlgebraicTopology.DoldKan.PInfty.f n

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites24

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.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement · cited by 8,081
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SimplexCategorystatement · cited by 2,204
HomologicalComplex.Xstatement · cited by 1,839
SSetstatement and proof · cited by 1,283
HomologicalComplex.Hom.fstatement and proof · cited by 845

Cited by2

Results whose statement or proof uses this declaration.

SSet.ιNormalizedChainComplex_fromNormalizedChainComplex_fproof · cited by 2
SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_f_assocproof · cited by 0