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+{-# OPTIONS --without-K --safe #-}
+
+open import Level using (Level; _⊔_)
+
+module NaturalTransformation.Instance.MultisetAppend {c ℓ : Level} where
+
+import Data.Opaque.List as L
+
+open import Categories.Category.BinaryProducts using (module BinaryProducts)
+open import Categories.Category.Cartesian using (Cartesian)
+open import Categories.Category.Monoidal.Instance.Setoids using (Setoids-Cartesian)
+open import Categories.Category.Product using (_※_)
+open import Categories.Functor using (Functor; _∘F_)
+open import Categories.NaturalTransformation using (NaturalTransformation; ntHelper)
+open import Data.List.Properties using (map-++)
+open import Data.List.Relation.Binary.Permutation.Setoid.Properties using (++⁺)
+open import Data.Opaque.Multiset using (Multisetₛ; mapₛ; ++ₛ)
+open import Data.Product using (_,_)
+open import Data.Product.Relation.Binary.Pointwise.NonDependent using (_×ₛ_)
+open import Function using (Func; _⟶ₛ_; _⟨$⟩_)
+open import Functor.Instance.Multiset {c} {ℓ} using (Multiset)
+open import Relation.Binary using (Setoid)
+
+open Cartesian (Setoids-Cartesian {c} {c ⊔ ℓ}) using (products)
+open BinaryProducts products using (-×-)
+open Func
+
+opaque
+  unfolding ++ₛ mapₛ
+
+  map-++ₛ
+    : {A B : Setoid c ℓ}
+      (f : Func A B)
+      (xs ys : Setoid.Carrier (Multiset.₀ A))
+    → (open Setoid (Multiset.₀ B))
+    → ++ₛ ⟨$⟩ (mapₛ f ⟨$⟩ xs , mapₛ f ⟨$⟩ ys) ≈ mapₛ f ⟨$⟩ (++ₛ ⟨$⟩ (xs , ys))
+  map-++ₛ {A} {B} f xs ys = sym (reflexive (map-++ (to f) xs ys))
+    where
+      open Setoid (Multiset.₀ B)
+
+++ : NaturalTransformation (-×- ∘F (Multiset ※ Multiset)) Multiset
+++ = ntHelper record
+    { η = λ X → ++ₛ
+    ; commute = λ { {A} {B} f {xs , ys} → map-++ₛ f xs ys }
+    }