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Theorems · Definition · algebraic topology

SSet.stdSimplex.face

{n : ℕ} → Finset (Fin (n + 1)) → (SSet.stdSimplex.obj { len := n }).Subcomplex

Given S : Finset (Fin (n + 1)), this is the corresponding face of Δ[n], as a subcomplex.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
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.

SSet.stdSimplex.faceSingletonComplIso · cited by 30stdSimplex.faceSingletonC…SSet.horn.multicoequalizerDiagram · cited by 16horn.multicoequalizerDiag…SSet.horn₃₁.desc.multicofork · cited by 10desc.multicoforkSSet.horn₃₂.desc.multicofork · cited by 10desc.multicoforkSSet.horn_eq_iSup · cited by 9SSet.horn_eq_iSupSSet.stdSimplex.facePairComplIso · cited by 9stdSimplex.facePairComplI…SSet.horn.isColimit · cited by 8horn.isColimitSSet.horn.faceSingletonComplIso_inv_ι · cited by 7horn.faceSingletonComplIs…SSet.stdSimplex.faceSingletonIso · cited by 7stdSimplex.faceSingletonI…SSet.stdSimplex.face_singleton_compl · cited by 6stdSimplex.face_singleton…SSet.horn.faceι · cited by 5horn.faceιSSet.stdSimplex.face_obj · cited by 5stdSimplex.face_objSSet.face_le_horn · cited by 5SSet.face_le_hornSSet.boundary.faceι · cited by 4boundary.faceιSSet.stdSimplex.facePairIso · cited by 4stdSimplex.facePairIsoDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objFinset · cited by 13712FinsetTop.top · cited by 9680Top.topOpposite · cited by 8081OppositeSet.ofPred · cited by 6101Set.ofPredSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetFinset.image · cited by 910Finset.imageSSet.stdSimplex · cited by 499SSet.stdSimplexSSet.Subcomplex · cited by 461SSet.SubcomplexSimplexCategory.Hom.toOrderHom · cited by 111Hom.toOrderHomSSet.stdSimplex.objEquiv · cited by 59stdSimplex.objEquivstdSimplex.faceCITED BYCITES

Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by87

Results whose statement or proof uses this declaration.