Theorems · Theorem · algebraic topology

SSet.Subcomplex.Pairing.ofIso_ancestralRel_iff

∀ {X : SSet} {A : X.Subcomplex} (P : A.Pairing) {Y : SSet} {B : Y.Subcomplex} (e : Y ≅ X) (hA : A.preimage e.hom = B)
  (x y : ↑P.II),
  (P.ofIso e hA).AncestralRel ⟨(SSet.Subcomplex.N.orderIsoOfIso e hA).symm ↑x, ⋯⟩
      ⟨(SSet.Subcomplex.N.orderIsoOfIso e hA).symm ↑y, ⋯⟩ ↔
    P.AncestralRel x y

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Pairing

Cited by

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Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound