Theorems · Theorem · algebraic topology

SSet.PInfty_toNormalizedChainComplex

∀ {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.CategoryStruct.comp AlgebraicTopology.DoldKan.PInfty (X.toNormalizedChainComplex R) =
    X.toNormalizedChainComplex R

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate
Cited by: 2 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive

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Cites23

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 and proof · 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
SSetstatement and proof · cited by 1,283
ComplexShape.downstatement · cited by 605
CategoryTheory.SimplicialObjectstatement · cited by 548

Cited by2

Results whose statement or proof uses this declaration.

SSet.toNormalizedChainComplex_normalizedChainComplexMapproof · cited by 2
SSet.PInfty_toNormalizedChainComplex_assocproof · cited by 0