Theorems · Theorem · algebraic topology
SSet.Subcomplex.eq_top_iff_contains_nonDegenerate
∀ {X : SSet} (A : X.Subcomplex), A = ⊤ ↔ ∀ (n : ℕ), X.nonDegenerate n ⊆ A.obj (Opposite.op { len := n })- Cited by
- 1 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- Set.Elemproof · cited by 7,166
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- CategoryTheory.Subfunctor.objstatement and proof · cited by 227
- SSet.nonDegeneratestatement and proof · cited by 106
- SSet.Subcomplex.le_iff_contains_nonDegenerateproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_topproof · cited by 1