Theorems · Theorem · algebraic topology
SSet.S.subcomplex_eq_of_epi
∀ {X : SSet} (x y : X.S) (f : { len := x.dim } ⟶ { len := y.dim }) [CategoryTheory.Epi f],
(CategoryTheory.ConcreteCategory.hom (X.map f.op)) y.simplex = x.simplex → x.subcomplex = y.subcomplex- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Epi
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- le_antisymmproof · cited by 2,068
- Quiver.Hom.opstatement and proof · cited by 1,948
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- CategoryTheory.Epistatement and proof · cited by 688
Cited by1
Results whose statement or proof uses this declaration.
- SSet.S.existsUnique_toNπproof · cited by 1