def Arrow.compose₁ : {α β γ : O} → Arrow β γ → Arrow α β → Arrow α γ :=
fun {α β γ} x x_1 =>
  match β, γ, x, x_1 with
  | β, .(β), Arrow.id, g => g
  | .(α), γ, f, Arrow.id => f
  | β, γ, Arrow.comp f₁ f₂, g => Arrow.comp f₁ (Arrow.comp f₂ g)
  | β, γ, f, g => Arrow.comp f g
Arrow.unit