Theorems · Definition · algebraic topology
SSet.spine
(X : SSet) → (n : ℕ) → X.obj (Opposite.op { len := n }) → X.Path nThe spine of an n-simplex in X is the path of edges of length n formed
by traversing in order through the vertices of X _⦋n⦌ₙ₊₁.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Pathstatement · cited by 46
- SSet.truncationproof · cited by 34
- SSet.Truncated.spineproof · cited by 24
Cited by34
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.spineIdproof · cited by 6
- SSet.StrictSegal.spine_spineToSimplex_applystatement · cited by 3
- SSet.StrictSegal.spineEquivproof · cited by 2
- SSet.spine_arrowstatement · cited by 2
- SSet.StrictSegal.spineToSimplex_intervalproof · cited by 1
- SSet.StrictSegal.spineToSimplex_spinestatement · cited by 1
- SSet.StrictSegal.spineToSimplex_spine_applystatement · cited by 1
- SSet.StrictSegal.spine_spineToSimplexstatement · cited by 1
- SSet.StrictSegal.spine_δ_arrow_eqstatement · cited by 1
- SSet.StrictSegal.spine_δ_arrow_gtstatement · cited by 1
- SSet.StrictSegal.spine_δ_arrow_ltstatement · cited by 1
- SSet.StrictSegalCore.spineToSimplexAuxstatement and proof · cited by 1