Theorems · Definition · algebraic topology
SSet.Subcomplex.PairingCore.simplex
{X : SSet} → {A : X.Subcomplex} → (self : A.PairingCore) → (s : self.ι) → X.obj (Opposite.op { len := self.dim s + 1 })the family of type (I) simplices
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.PairingCorestatement and proof · cited by 50
- SSet.Subcomplex.PairingCore.ιstatement · cited by 42
- SSet.Subcomplex.PairingCore.dimstatement · cited by 22
Cited by15
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.PairingCore.type₁proof · cited by 13
- SSet.Subcomplex.PairingCore.type₂proof · cited by 12
- SSet.Subcomplex.PairingCore.surjective'statement · cited by 1
- SSet.Subcomplex.PairingCore.injective_type₁'statement · cited by 1
- SSet.Subcomplex.PairingCore.injective_type₂'statement · cited by 1
- SSet.Subcomplex.PairingCore.type₁_ne_type₂'statement · cited by 1
- SSet.Subcomplex.PairingCore.type₁_simplexstatement · cited by 1
- SSet.Subcomplex.PairingCore.type₂_simplexstatement · cited by 1
- SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace_indexproof · cited by 1
- SSet.prodStdSimplex.pairingCore_simplexstatement and proof · cited by 0
- SSet.Subcomplex.PairingCore.surjectiveproof · cited by 0
- SSet.Subcomplex.PairingCore.nonDegenerate₁statement · cited by 0