1 files changed, 35 insertions, 0 deletions
diff --git a/NaturalTransformation/Instance/EmptyList.agda b/NaturalTransformation/Instance/EmptyList.agda
new file mode 100644
index 0000000..9f94955
--- /dev/null
+++ b/NaturalTransformation/Instance/EmptyList.agda
@@ -0,0 +1,35 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Level using (Level; _⊔_)
+
+module NaturalTransformation.Instance.EmptyList {c ℓ : Level} where
+
+open import Categories.Functor using (Functor)
+open import Categories.Functor.Construction.Constant using (const)
+open import Categories.NaturalTransformation using (NaturalTransformation; ntHelper)
+open import Data.Opaque.List using (Listₛ; []ₛ; mapₛ)
+open import Data.Setoid using (_⇒ₛ_)
+open import Data.Setoid.Unit using (⊤ₛ)
+open import Function using (_⟶ₛ_)
+open import Function.Construct.Constant using () renaming (function to Const)
+open import Function.Construct.Setoid using (_∙_)
+open import Functor.Instance.List {c} {ℓ} using (List)
+open import Relation.Binary using (Setoid)
+
+opaque
+
+  unfolding []ₛ
+
+  map-[]ₛ : {A B : Setoid c ℓ}
+      → (f : A ⟶ₛ B)
+      → (open Setoid (⊤ₛ ⇒ₛ Listₛ B))
+      → []ₛ ≈ mapₛ f ∙ []ₛ
+  map-[]ₛ {_} {B} f = refl
+    where
+      open Setoid (List.₀ B)
+
+⊤⇒[] : NaturalTransformation (const ⊤ₛ) List
+⊤⇒[] = ntHelper record
+    { η = λ X → []ₛ
+    ; commute = map-[]ₛ
+    }