Theorems · Definition · algebraic topology
SSet.boundary
(n : ℕ) → (SSet.stdSimplex.obj { len := n }).SubcomplexThe boundary ∂Δ[n] of the n-th standard simplex consists of
all m-simplices of stdSimplex n that are not surjective
(when viewed as monotone function m → n).
- Cited by
- 141 results in Mathlib
- Foundations
- Depth 35 from the axioms, rests on 362 definitions · 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.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- 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
- SSet.stdSimplexstatement and proof · cited by 499
- SSet.Subcomplexstatement · cited by 461
- SSet.stdSimplex.asOrderHomproof · cited by 7
Cited by181
Results whose statement or proof uses this declaration.
- SSet.PtSimplexproof · cited by 41
- SSet.prodStdSimplex.pairingCore.IsIndexstatement and proof · cited by 26
- SSet.prodStdSimplex.pairingCore.minstatement and proof · cited by 18
- SSet.relativeCellComplexOfMonostatement and proof · cited by 14
- SSet.prodStdSimplex.pairingCore.IsType₂.φstatement and proof · cited by 14
- SSet.prodStdSimplex.pairingCore.IsType₂statement and proof · cited by 14
- SSet.relativeCellComplexOfMono.sigmaBoundaryproof · cited by 11
- SSet.prodStdSimplex.pairingCore.Type₁.xstatement · cited by 10
- SSet.relativeCellComplexOfMono.lproof · cited by 8
- SSet.prodStdSimplex.pairingCore.IsIndex.δstatement and proof · cited by 7
- SSet.prodStdSimplex.pairingCore.IsType₂.simplexstatement and proof · cited by 7
- SSet.prodStdSimplex.pairingCore.finsetstatement and proof · cited by 7