Theorems · Definition · algebraic topology
SSet.Subcomplex.PairingCore.equivII
{X : SSet} → {A : X.Subcomplex} → (h : A.PairingCore) → h.ι ≃ ↑h.IIThe bijection h.ι ≃ h.II when h : A.PairingCore.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 45 from the axioms · 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.
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.Nstatement · cited by 155
- Equiv.ofInjectiveproof · cited by 64
- SSet.Subcomplex.PairingCorestatement and proof · cited by 50
- SSet.Subcomplex.PairingCore.ιstatement · cited by 42
- SSet.Subcomplex.PairingCore.type₂proof · cited by 12
- SSet.Subcomplex.PairingCore.IIstatement · cited by 6
- SSet.Subcomplex.PairingCore.injective_type₂proof · cited by 0
Cited by10
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.PairingCore.pairingproof · cited by 11
- SSet.Subcomplex.PairingCore.isRegular_pairing_iffproof · cited by 4
- SSet.Subcomplex.PairingCore.rankFunctionEquivproof · cited by 2
- SSet.Subcomplex.PairingCore.weakRankFunctionEquivproof · cited by 2
- SSet.Subcomplex.PairingCore.pairing_p_equivIIstatement and proof · cited by 2
- SSet.Subcomplex.PairingCore.equivII_apply_coestatement and proof · cited by 1
- SSet.Subcomplex.PairingCore.type₁_pairingstatement · cited by 1
- SSet.Subcomplex.PairingCore.isProper_pairing_iffproof · cited by 1
- SSet.Subcomplex.PairingCore.pairing_p_symm_equivIstatement and proof · cited by 0
- SSet.Subcomplex.PairingCore.ancestralRel_iffstatement and proof · cited by 0