Theorems · Definition · algebraic topology
SSet.Truncated.Path.arrow
{n : ℕ} →
{X : SSet.Truncated (n + 1)} → {m : ℕ} → X.Path m → Fin m → X.obj (Opposite.op { obj := { len := 1 }, property := ⋯ })A path includes the data of n 1-simplices in X.
- Cited by
- 20 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 and proof · cited by 37
- SSet.Truncated.Path₁.arrowproof · cited by 8
Cited by24
Results whose statement or proof uses this declaration.
- SSet.Path.arrowproof · cited by 27
- SSet.Truncated.Path.ext'statement and proof · cited by 6
- SSet.Truncated.Path.intervalproof · cited by 5
- SSet.Truncated.Path.mk₂proof · cited by 5
- SSet.Truncated.Path.extstatement and proof · cited by 4
- SSet.Truncated.Path.mapproof · cited by 4
- SSet.Truncated.spine_arrowstatement · cited by 4
- SSet.Truncated.StrictSegal.spineToSimplex_arrowstatement and proof · cited by 3
- SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_onestatement and proof · cited by 3
- SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_zerostatement and proof · cited by 3
- SSet.Truncated.Path.arrow_srcstatement · cited by 2
- SSet.Truncated.Path.arrow_tgtstatement · cited by 2