module SOAS.Families.Delta {T : Set} where
open import SOAS.Common
open import SOAS.Context
open import SOAS.Variable
open import SOAS.Sorting
open import SOAS.Construction.Structure
open import SOAS.Families.Core {T}
module Unsorted where
δ : Ctx → Family → Family
δ Θ X Γ = X (Θ ∔ Γ)
δF : Ctx → Functor 𝔽amilies 𝔽amilies
δF Θ = record { F₀ = δ Θ ; F₁ = λ f → f ; identity = refl
; homomorphism = refl ; F-resp-≈ = λ z → z }
δ₁ : T → Family → Family
δ₁ τ = δ ⌈ τ ⌋
δ₁F_ : T → Functor 𝔽amilies 𝔽amilies
δ₁F τ = δF ⌈ τ ⌋
private
variable
Γ Δ : Ctx
α : T
module Sorted where
δ : Ctx → Familyₛ → Familyₛ
δ Θ 𝒳 α Γ = 𝒳 α (Θ ∔ Γ)
δF : Ctx → Functor 𝔽amiliesₛ 𝔽amiliesₛ
δF Θ = record { F₀ = δ Θ ; F₁ = λ f → f ; identity = refl
; homomorphism = refl ; F-resp-≈ = λ z → z }
δ₁ : T → Familyₛ → Familyₛ
δ₁ τ = δ ⌈ τ ⌋
δ₁F_ : T → Functor 𝔽amiliesₛ 𝔽amiliesₛ
δ₁F τ = δF ⌈ τ ⌋