Mathlib Map

Theorems · Definition · algebraic topology

SSet.S.simplex

{X : SSet} → (self : X.S) → X.obj (Opposite.op { len := self.dim })

the simplex

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Simplices
Cited by
111 results in Mathlib
Foundations
Depth 34 from the axioms, rests on 273 definitions · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.S.subcomplex · cited by 39S.subcomplexSSet.S.cast · cited by 35S.castSSet.prodStdSimplex.pairingCore.IsIndex · cited by 26pairingCore.IsIndexSSet.S.IsUniquelyCodimOneFace · cited by 19S.IsUniquelyCodimOneFaceSSet.prodStdSimplex.pairingCore.IsType₂.φ · cited by 14IsType₂.φSSet.Subcomplex.Pairing.RankFunction.Cell.map · cited by 12Cell.mapSSet.N.nonDegenerate · cited by 11N.nonDegenerateSSet.prodStdSimplex.pairingCore.IsIndex.δ · cited by 7IsIndex.δSSet.S.IsUniquelyCodimOneFace.δ_index · cited by 7IsUniquelyCodimOneFace.δ_…SSet.Subcomplex.N.notMem · cited by 7N.notMemSSet.S.mk_surjective · cited by 7S.mk_surjectiveSSet.prodStdSimplex.pairingCore.finset · cited by 7pairingCore.finsetSSet.prodStdSimplex.pairingCore · cited by 6prodStdSimplex.pairingCoreSSet.S.equivElements · cited by 5S.equivElementsSSet.prodStdSimplex.pairingCore.IsIndex.simplex_fst_succ · cited by 4IsIndex.simplex_fst_succCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.S.dim · cited by 162S.dimSSet.S · cited by 69SSet.SS.simplexCITED BYCITES

Cites6

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

Cited by142

Results whose statement or proof uses this declaration.