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Theorems · Definition · algebraic topology

SSet.Truncated.Path.vertex

{n : ℕ} →
  {X : SSet.Truncated (n + 1)} →
    {m : ℕ} → X.Path m → Fin (m + 1) → X.obj (Opposite.op { obj := { len := 0 }, property := ⋯ })

A path includes the data of n + 1 0-simplices in X.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Path
Cited by
16 results in Mathlib
Foundations
Depth 55 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.Path.vertex · cited by 19Path.vertexSSet.Truncated.Path.ext' · cited by 6Path.ext'SSet.Truncated.Path.interval · cited by 5Path.intervalSSet.Truncated.Path.mk₂ · cited by 5Path.mk₂SSet.Truncated.Path.ext · cited by 4Path.extSSet.Truncated.Path.map · cited by 4Path.mapSSet.Truncated.spine_vertex · cited by 3Truncated.spine_vertexSSet.Truncated.Path.arrow_src · cited by 2Path.arrow_srcSSet.Truncated.Path.arrow_tgt · cited by 2Path.arrow_tgtSSet.Truncated.StrictSegal.spineToSimplex_vertex · cited by 2StrictSegal.spineToSimple…SSet.Truncated.Path.mk₂_arrow · cited by 2Path.mk₂_arrowSSet.Truncated.spine_map_subinterval · cited by 2Truncated.spine_map_subin…SSet.Truncated.spine_map_vertex · cited by 1Truncated.spine_map_vertexSSet.spine_δ₀ · cited by 1SSet.spine_δ₀SSet.Truncated.Path.ext_iff · cited by 0Path.ext_iffCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSSet.Truncated.Path · cited by 37Truncated.PathSSet.Truncated.Path₁.vertex · cited by 8Path₁.vertexPath.vertexCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.