Theorems · Definition · algebraic topology
SSet.Path.vertex
{X : SSet} → {n : ℕ} → X.Path n → Fin (n + 1) → X.obj (Opposite.op { len := 0 })A path includes the data of n + 1 0-simplices in X.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SSetstatement and proof · cited by 1,283
- SSet.Pathstatement and proof · cited by 46
- SSet.Truncated.Path.vertexproof · cited by 16
Cited by21
Results whose statement or proof uses this declaration.
- SSet.StrictSegal.spineToSimplex_vertexstatement and proof · cited by 3
- SSet.Subcomplex.liftPathstatement and proof · cited by 3
- SSet.Path.extstatement and proof · cited by 2
- SSet.Path.ext₀statement and proof · cited by 2
- SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂proof · cited by 1
- SSet.StrictSegalCore.spineToSimplexAuxproof · cited by 1
- SSet.spine_vertexstatement · cited by 1
- SSet.StrictSegal.spine_δ_vertex_gestatement and proof · cited by 0
- SSet.StrictSegal.spine_δ_vertex_ltstatement and proof · cited by 0
- SSet.Subcomplex.liftPath_arrow_coestatement and proof · cited by 0
- SSet.StrictSegalCore.spineToSimplex_zerostatement · cited by 0
- SSet.stdSimplex.spineId_vertexstatement · cited by 0