Theorems · Inductive type · algebraic topology
SSet.Subcomplex.Pairing.RankFunction
{X : SSet} → {A : X.Subcomplex} → A.Pairing → (α : Type v) → [PartialOrder α] → Type (max u v)A rank function for a pairing is a function from the type (II) simplices to a partially ordered type which maps ancestrality relations to strict inequalities.
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement · cited by 6,410
- SSetstatement · cited by 1,283
- SSet.Subcomplexstatement · cited by 461
- SSet.Subcomplex.Pairingstatement · cited by 117
Cited by105
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.Pairing.RankFunction.Cellstatement · cited by 55
- SSet.Subcomplex.Pairing.RankFunction.Cell.dimstatement and proof · cited by 40
- SSet.Subcomplex.Pairing.RankFunction.filtrationstatement and proof · cited by 34
- SSet.Subcomplex.Pairing.RankFunction.Cell.sstatement and proof · cited by 21
- SSet.Subcomplex.Pairing.RankFunction.sigmaStdSimplexstatement and proof · cited by 21
- SSet.Subcomplex.Pairing.RankFunction.Cell.hornstatement and proof · cited by 19
- SSet.Subcomplex.Pairing.RankFunction.sigmaHornstatement and proof · cited by 18
- SSet.Subcomplex.Pairing.RankFunction.Cell.ιSigmaStdSimplexstatement and proof · cited by 16
- SSet.Subcomplex.Pairing.RankFunction.bstatement and proof · cited by 13
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapstatement and proof · cited by 12
- SSet.Subcomplex.Pairing.RankFunction.mstatement and proof · cited by 12
- SSet.Subcomplex.Pairing.RankFunction.Cell.indexstatement and proof · cited by 10