Theorems · Theorem · algebraic topology

SSet.S.eq_iff_ofSimplex_eq

∀ {X : SSet} {n m : ℕ} (x : X.obj (Opposite.op { len := n })) (y : X.obj (Opposite.op { len := m })),
  x ∈ X.nonDegenerate n →
    y ∈ X.nonDegenerate m →
      ({ dim := n, simplex := x } = { dim := m, simplex := y } ↔
        SSet.Subcomplex.ofSimplex x = SSet.Subcomplex.ofSimplex y)

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound