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.
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SimplexCategory.lenstatement · cited by 542
- SimplexCategory.Truncatedstatement · cited by 236
- SSet.Truncatedstatement and proof · cited by 214
- SSet.Truncated.Pathstatement · cited by 37
- SSet.Truncated.StrictSegalstatement and proof · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- SSet.Truncated.StrictSegal.spineEquivproof · cited by 6
- SSet.Truncated.StrictSegal.spineToSimplex_arrowstatement and proof · cited by 3
- SSet.Truncated.StrictSegal.spine_spineToSimplex_applystatement · cited by 3
- SSet.Truncated.StrictSegal.spineToDiagonalproof · cited by 2
- SSet.Truncated.StrictSegal.spineToSimplex_vertexstatement and proof · cited by 2
- SSet.Truncated.StrictSegal.spineToSimplex_edgestatement and proof · cited by 1
- SSet.Truncated.StrictSegal.spineToSimplex_intervalstatement and proof · cited by 1
- SSet.Truncated.StrictSegal.spineToSimplex_spinestatement · cited by 1
- SSet.Truncated.StrictSegal.spine_spineToSimplexstatement · cited by 1
- SSet.Truncated.StrictSegal.spineToSimplex_mapstatement and proof · cited by 0
- SSet.Truncated.StrictSegal.spineToSimplex_spine_applystatement · cited by 0
- SSet.Truncated.StrictSegal.spine_δ_arrow_eqstatement and proof · cited by 0