Theorems · Definition · algebraic topology

SSet.stdSimplex.facePairComplIso

{n : ℕ} → (i j : Fin (n + 3)) → i < j → (SSet.stdSimplex.obj { len := n } ≅ (SSet.stdSimplex.face {i, j}ᶜ).toSSet)

If i < j are in Fin (n + 3), this is the isomorphism between Δ[n] and the face of Δ[n + 2] corresponding to {i, j}ᶜ.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex

Cited by

9 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound