Theorems · Definition · algebraic topology
SSet.stdSimplex.face
{n : ℕ} → Finset (Fin (n + 1)) → (SSet.stdSimplex.obj { len := n }).SubcomplexGiven S : Finset (Fin (n + 1)), this is the corresponding face of Δ[n],
as a subcomplex.
- Cited by
- 77 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Finsetstatement and proof · cited by 13,712
- Top.topproof · cited by 9,680
- Oppositestatement and proof · cited by 8,081
- Set.ofPredproof · cited by 6,101
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement · cited by 1,283
- Finset.imageproof · cited by 910
- SSet.stdSimplexstatement and proof · cited by 499
- SSet.Subcomplexstatement · cited by 461
Cited by87
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.faceSingletonComplIsostatement · cited by 30
- SSet.horn.multicoequalizerDiagramstatement and proof · cited by 16
- SSet.horn₃₁.desc.multicoforkstatement · cited by 10
- SSet.horn₃₂.desc.multicoforkstatement · cited by 10
- SSet.horn_eq_iSupstatement and proof · cited by 9
- SSet.stdSimplex.facePairComplIsostatement · cited by 9
- SSet.horn.isColimitstatement · cited by 8
- SSet.horn.faceSingletonComplIso_inv_ιstatement · cited by 7
- SSet.stdSimplex.faceSingletonIsostatement · cited by 7
- SSet.stdSimplex.face_singleton_complstatement · cited by 6
- SSet.horn.faceιstatement · cited by 5
- SSet.stdSimplex.face_objstatement and proof · cited by 5