Theorems · Theorem · algebraic topology
SSet.exists_nonDegenerate
∀ (X : SSet) {n : ℕ} (x : X.obj (Opposite.op { len := n })),
∃ m f, ∃ (_ : CategoryTheory.Epi f), ∃ y, x = (CategoryTheory.ConcreteCategory.hom (X.map f.op)) ↑y- Cited by
- 4 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- Quiver.Hom.opstatement and proof · cited by 1,948
Cited by4
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.le_iff_contains_nonDegenerateproof · cited by 7
- SSet.mem_skeletonproof · cited by 4
- SSet.S.existsUnique_nproof · cited by 2
- SSet.S.existsUnique_toNπproof · cited by 1