Theorems · Theorem · algebraic topology
SSet.Subcomplex.ofSimplex_le_iff
∀ {X : SSet} {n : ℕ} (x : X.obj (Opposite.op { len := n })) (A : X.Subcomplex),
SSet.Subcomplex.ofSimplex x ≤ A ↔ x ∈ A.obj (Opposite.op { len := n })- Cited by
- 8 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- CategoryTheory.Subfunctor.objstatement · cited by 227
- SSet.Subcomplex.ofSimplexstatement · cited by 73
- CategoryTheory.Subfunctor.ofSection_le_iffproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- SSet.S.le_iffproof · cited by 2
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_image_hornproof · cited by 2
- SSet.subcomplex_le_horn_iffproof · cited by 2
- SSet.boundary_obj_eq_univproof · cited by 1
- SSet.Subcomplex.image_ofSimplexproof · cited by 1
- SSet.objEquiv_symm_δ_mem_horn_iffproof · cited by 1
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_filtrationproof · cited by 1
- SSet.stdSimplex.nonDegenerateEquiv'_symm_mem_iff_face_leproof · cited by 0