Theorems · Definition · algebraic topology
SSet.horn
(n : ℕ) → Fin (n + 1) → (SSet.stdSimplex.obj { len := n }).Subcomplexhorn n i (or Λ[n, i]) is the i-th horn of the n-th standard simplex,
where i : n. It consists of all m-simplices α of Δ[n]
for which the union of {i} and the range of α is not all of n
(when viewing α as monotone function m → n).
- Cited by
- 162 results in Mathlib
- Foundations
- Depth 36 from the axioms, rests on 411 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- 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 by214
Results whose statement or proof uses this declaration.
- SSet.prodStdSimplex.pairingCore.IsIndexstatement and proof · cited by 26
- SSet.Subcomplex.Pairing.RankFunction.Cell.hornproof · cited by 19
- SSet.prodStdSimplex.pairingCore.minstatement and proof · cited by 18
- SSet.horn.multicoequalizerDiagramstatement · cited by 16
- SSet.prodStdSimplex.pairingCore.IsType₂.φstatement and proof · cited by 14
- SSet.prodStdSimplex.pairingCore.IsType₂statement and proof · cited by 14
- SSet.horn.ιstatement · cited by 13
- SSet.modelCategoryQuillen.Jproof · cited by 12
- SSet.prodStdSimplex.pairingCore.Type₁.xstatement · cited by 10
- SSet.horn₃₁.desc.multicoforkstatement · cited by 10
- SSet.horn₃₂.desc.multicoforkstatement · cited by 10
- SSet.horn_eq_iSupstatement · cited by 9
Showing the 200 most cited of 214.