Theorems · Theorem · algebraic topology
SSet.StrictSegal.spineToSimplex_vertex
∀ {X : SSet} (sx : X.StrictSegal) {n : ℕ} (i : Fin (n + 1)) (f : X.Path n),
(CategoryTheory.ConcreteCategory.hom (X.map ({ len := 0 }.const { len := n } i).op)) (sx.spineToSimplex f) =
f.vertex i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapstatement · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- Quiver.Hom.opstatement · cited by 1,948
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- SimplexCategory.conststatement · cited by 47
- SSet.Pathstatement and proof · cited by 46
- SSet.StrictSegalstatement and proof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- SSet.StrictSegal.isPointwiseRightKanExtensionAt.fac_aux₂proof · cited by 1
- SSet.StrictSegal.spine_δ_vertex_geproof · cited by 0
- SSet.StrictSegal.spine_δ_vertex_ltproof · cited by 0