Theorems · Theorem · algebraic topology
SSet.mono_of_nonDegenerate
∀ (X : SSet) {n : ℕ} (x : ↑(X.nonDegenerate n)) {m : SimplexCategory} (f : { len := n } ⟶ m)
(y : X.obj (Opposite.op m)), (CategoryTheory.ConcreteCategory.hom (X.map f.op)) y = ↑x → CategoryTheory.Mono f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- SimplexCategorystatement and proof · 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
Cited by3
Results whose statement or proof uses this declaration.
- SSet.N.le_iff_exists_monoproof · cited by 3
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_image_hornproof · cited by 2
- SSet.mem_skeleton_obj_iff_of_nonDegenerateproof · cited by 1