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Theorems · Theorem · algebraic topology

SSet.Truncated.StrictSegal.spineToSimplex_arrow

∀ {n : ℕ} {X : SSet.Truncated (n + 1)} (sx : X.StrictSegal) (m : ℕ) (h : m ≤ n + 1) (i : Fin m) (f : X.Path m),
  (CategoryTheory.ConcreteCategory.hom (X.map (SimplexCategory.Truncated.Hom.tr (SimplexCategory.mkOfSucc i) ⋯ h).op))
      (sx.spineToSimplex m h f) =
    f.arrow i
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal
Cited by
3 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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SSet.Truncated.StrictSegal.spine_δ_arrow_gt · cited by 0StrictSegal.spine_δ_arrow…SSet.Truncated.StrictSegal.spineToSimplex_map · cited by 0StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_δ_arrow_lt · cited by 0StrictSegal.spine_δ_arrow…DFunLike.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.FunCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…SimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSimplexCategory.Truncated.Hom.tr · cited by 43Hom.trSimplexCategory.mkOfSucc · cited by 38SimplexCategory.mkOfSuccSSet.Truncated.Path · cited by 37Truncated.PathStrictSegal.spineToSimplex_ar…CITED BYCITES

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