Theorems · Theorem · algebraic topology
SSet.Subcomplex.le_iff_of_hasDimensionLT
∀ {X : SSet} (A B : X.Subcomplex) (d : ℕ) [X.HasDimensionLT d],
A ≤ B ↔ ∀ i < d, A.obj (Opposite.op { len := i }) ∩ X.nonDegenerate i ⊆ B.obj (Opposite.op { len := i })- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SSet.HasDimensionLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.Elemproof · cited by 7,166
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- Subtype.propproof · cited by 505
- SSet.Subcomplexstatement and proof · cited by 461
- CategoryTheory.Subfunctor.objstatement and proof · cited by 227
- SSet.nonDegeneratestatement and proof · cited by 106
- SSet.HasDimensionLTstatement and proof · cited by 32
- SSet.Subcomplex.le_iff_contains_nonDegenerateproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.eq_top_iff_of_hasDimensionLTproof · cited by 0