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Theorems · Theorem · algebraic topology

SSet.spine_arrow

∀ (X : SSet) (n : ℕ) (Δ : X.obj (Opposite.op { len := n })) (i : Fin n),
  (X.spine n Δ).arrow i = (CategoryTheory.ConcreteCategory.hom (X.map (SimplexCategory.mkOfSucc i).op)) Δ
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Path
Cited by
2 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

SSet.StrictSegal.spineToSimplex_arrow · cited by 4StrictSegal.spineToSimple…SSet.StrictSegal.quasicategory · cited by 0StrictSegal.quasicategoryDFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opTypeCat.Fun · cited by 1307TypeCat.FunSSet · cited by 1283SSetSimplexCategory.mkOfSucc · cited by 38SimplexCategory.mkOfSuccSSet.Path.arrow · cited by 27Path.arrowSSet.spine · cited by 23SSet.spineSSet.spine_arrowCITED BYCITES

Cites12

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Cited by2

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