Theorems · Theorem · algebraic topology
SSet.S.IsUniquelyCodimOneFace.unique
∀ {X : SSet} {x y : X.S} (hxy : x.IsUniquelyCodimOneFace y) {d : ℕ} (hd : x.dim = d)
(f : { len := d } ⟶ { len := d + 1 }) [CategoryTheory.Mono f],
(CategoryTheory.ConcreteCategory.hom (X.map f.op)) (y.cast ⋯).simplex = (x.cast hd).simplex →
f = SimplexCategory.δ (hxy.index hd)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- Quiver.Hom.opstatement and proof · cited by 1,948
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- CategoryTheory.Monostatement and proof · cited by 893
- SSet.S.dimstatement and proof · cited by 162
Cited by1
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_image_hornproof · cited by 2