Mathlib Map

Theorems · Definition · algebraic topology

SSet.Truncated.StrictSegal.spineToSimplex

{n : ℕ} →
  {X : SSet.Truncated (n + 1)} →
    X.StrictSegal →
      (m : ℕ) →
        (h : autoParam (m ≤ n + 1) SSet.Truncated.StrictSegal._auto_1) →
          X.Path m → X.obj (Opposite.op { obj := { len := m }, property := h })

The inverse to spine X m.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal
Cited by
14 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

SSet.Truncated.StrictSegal.spineEquiv · cited by 6StrictSegal.spineEquivSSet.Truncated.StrictSegal.spineToSimplex_arrow · cited by 3StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_spineToSimplex_apply · cited by 3StrictSegal.spine_spineTo…SSet.Truncated.StrictSegal.spineToDiagonal · cited by 2StrictSegal.spineToDiagon…SSet.Truncated.StrictSegal.spineToSimplex_vertex · cited by 2StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spineToSimplex_edge · cited by 1StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spineToSimplex_interval · cited by 1StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spineToSimplex_spine · cited by 1StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_spineToSimplex · cited by 1StrictSegal.spine_spineTo…SSet.Truncated.StrictSegal.spineToSimplex_map · cited by 0StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spineToSimplex_spine_apply · cited by 0StrictSegal.spineToSimple…SSet.Truncated.StrictSegal.spine_δ_arrow_eq · cited by 0StrictSegal.spine_δ_arrow…SSet.Truncated.StrictSegal.spine_δ_arrow_gt · cited by 0StrictSegal.spine_δ_arrow…SSet.Truncated.StrictSegal.spine_δ_arrow_lt · cited by 0StrictSegal.spine_δ_arrow…SSet.Truncated.StrictSegal.spine_δ_vertex_ge · cited by 0StrictSegal.spine_δ_verte…CategoryTheory.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.StrictSegal · cited by 30Truncated.StrictSegalStrictSegal.spineToSimplexCITED BYCITES

Cites8

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

Cited by16

Results whose statement or proof uses this declaration.