nonDegenerateEquivOfIso — Mathlib

English

There is a natural bijection between X.nonDegenerate(n) and Y.nonDegenerate(n) induced by an isomorphism e: X ≅ Y.

Русский

Существует натуральная биекция между ненегидными n-симплексами X и Y, индуцируемая изоморфизмом e: X ≅ Y.

LaTeX

$$$$X.nonDegenerate(n) \cong Y.nonDegenerate(n) \text{ via } e,$$$$

Lean4

/-- The bijection on nondegenerate simplices induced by an isomorphism
of simplicial sets. -/
@[simps]
def nonDegenerateEquivOfIso (e : X ≅ Y) {n : ℕ} : X.nonDegenerate n ≃ Y.nonDegenerate n
    where
  toFun := fun ⟨x, hx⟩ ↦ ⟨e.hom.app _ x, by aesop⟩
  invFun := fun ⟨y, hy⟩ ↦ ⟨e.inv.app _ y, by aesop⟩
  left_inv _ := by aesop
  right_inv _ := by aesop

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