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Theorems · Definition · algebraic topology

SSet.Truncated.StrictSegal.spineToDiagonal

{n : ℕ} →
  {X : SSet.Truncated (n + 1)} →
    X.StrictSegal →
      (m : ℕ) → autoParam (m ≤ n + 1) _auto_41✝ → X.Path m → X.obj (Opposite.op { obj := { len := 1 }, property := ⋯ })

In the presence of the strict Segal condition, a path of length m can be "composed" by taking the diagonal edge of the resulting m-simplex.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal
Cited by
2 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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SSet.Truncated.StrictSegal.spineToSimplex_edge · cited by 1StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_δ_arrow_eq · 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.opSimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSimplexCategory.Truncated.Hom.tr · cited by 43Hom.trSSet.Truncated.Path · cited by 37Truncated.PathSSet.Truncated.StrictSegal · cited by 30Truncated.StrictSegalSSet.Truncated.StrictSegal.spineToSimplex · cited by 14StrictSegal.spineToSimplexSimplexCategory.diag · cited by 4SimplexCategory.diagStrictSegal.spineToDiagonalCITED BYCITES

Cites15

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Cited by2

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