Theorems · Definition · algebraic topology
SSet.Subcomplex.Pairing.ofIso
{X : SSet} →
{A : X.Subcomplex} → A.Pairing → {Y : SSet} → {B : Y.Subcomplex} → (e : Y ≅ X) → A.preimage e.hom = B → B.PairingGiven an isomorphism Y ≅ X of simplicial sets, a pairing P of a subcomplex
A of X, this is a pairing for a subcomplex B of Y if A.preimage e.hom = B.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- Set.preimageproof · cited by 4,946
- CategoryTheory.Isostatement and proof · cited by 3,963
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- OrderIso.symmproof · cited by 475
- SSet.Subcomplexstatement and proof · cited by 461
- Equiv.transproof · cited by 337
- SSet.Subcomplex.Pairingstatement and proof · cited by 117
- RelIso.toEquivproof · cited by 113
Cited by8
Results whose statement or proof uses this declaration.
- SSet.prodStdSimplex.pairingproof · cited by 4
- SSet.Subcomplex.Pairing.ofIso_pstatement · cited by 2
- SSet.Subcomplex.Pairing.strongInnerAnodyneExtensionsproof · cited by 1
- SSet.Subcomplex.Pairing.ofIso.congr_simpstatement and proof · cited by 0
- SSet.Subcomplex.Pairing.ofIso_Istatement and proof · cited by 0
- SSet.Subcomplex.Pairing.ofIso_IIstatement and proof · cited by 0
- SSet.Subcomplex.Pairing.ofIso_ancestralRel_iffstatement · cited by 0
- SSet.Subcomplex.Pairing.ofIso_indexstatement and proof · cited by 0