Theorems · Definition · algebraic topology
SSet.stdSimplex.faceSingletonComplIso
{n : ℕ} → (i : Fin (n + 2)) → SSet.stdSimplex.obj { len := n } ≅ (SSet.stdSimplex.face {i}ᶜ).toSSetIn Δ[n + 1], the face corresponding to the complement of {i}
for i : Fin (n + 2) is isomorphic to Δ[n].
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Finsetstatement · cited by 13,712
- Oppositestatement · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- Compl.complstatement and proof · cited by 2,925
- SimplexCategorystatement · cited by 2,204
- SSetstatement · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.stdSimplex.facestatement · cited by 77
- SSet.stdSimplex.faceRepresentableByproof · cited by 1
- SSet.stdSimplex.isoOfRepresentableByproof · cited by 1
Cited by32
Results whose statement or proof uses this declaration.
- SSet.horn₃₂.desc.multicoforkproof · cited by 10
- SSet.horn₃₁.desc.multicoforkproof · cited by 10
- SSet.horn.faceSingletonComplIso_inv_ιstatement and proof · cited by 7
- SSet.horn.faceSingletonComplIso_inv_ι_assocstatement and proof · cited by 2
- SSet.horn.hom_ext'proof · cited by 2
- SSet.horn₃₁.ι₀_descproof · cited by 2
- SSet.horn₃₁.ι₂_descproof · cited by 2
- SSet.horn₃₁.ι₃_descproof · cited by 2
- SSet.horn₃₂.ι₀_descproof · cited by 2
- SSet.horn₃₂.ι₁_descproof · cited by 2
- SSet.horn₃₂.ι₃_descproof · cited by 2
- SSet.stdSimplex.faceSingletonComplIso_hom_ιstatement · cited by 1