Theorems · Theorem · algebraic topology
SSet.Subcomplex.le_iff_contains_nonDegenerate
∀ {X : SSet} (A B : X.Subcomplex),
A ≤ B ↔
∀ (n : ℕ) (x : ↑(X.nonDegenerate n)), ↑x ∈ A.obj (Opposite.op { len := n }) → ↑x ∈ B.obj (Opposite.op { len := n })- Cited by
- 7 results in Mathlib
- Foundations
- Depth 85 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.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- SimplexCategorystatement and proof · cited by 2,204
- Quiver.Hom.opproof · cited by 1,948
- SSetstatement and proof · cited by 1,283
- CategoryTheory.Epiproof · cited by 688
Cited by7
Results whose statement or proof uses this declaration.
- SSet.N.subcomplex_le_iffproof · cited by 2
- SSet.subcomplex_le_horn_iffproof · cited by 2
- SSet.stdSimplex.le_boundary_iffproof · cited by 2
- SSet.Subcomplex.le_iff_of_hasDimensionLTproof · cited by 1
- SSet.Subcomplex.eq_top_iff_contains_nonDegenerateproof · cited by 1
- SSet.iSup_skeletonproof · cited by 1
- SSet.relativeCellComplexOfMono.Cell.preimage_mapproof · cited by 1