From 5f4d1cf740591476d3c7bc270fd11a2c578ab7e6 Mon Sep 17 00:00:00 2001
From: Jacques Comeaux <jacquesrcomeaux@protonmail.com>
Date: Wed, 5 Nov 2025 08:11:48 -0600
Subject: Adjust universe levels

---
 Functor/Instance/Nat/Circ.agda                | 22 ++++++++--------
 Functor/Instance/Nat/Edge.agda                | 20 +++++----------
 Functor/Instance/Nat/System.agda              | 10 ++++----
 Functor/Monoidal/Construction/ListOf.agda     |  4 +--
 Functor/Monoidal/Construction/MultisetOf.agda |  4 +--
 Functor/Monoidal/Instance/Nat/System.agda     | 36 +++++++++++++++------------
 6 files changed, 46 insertions(+), 50 deletions(-)

(limited to 'Functor')

diff --git a/Functor/Instance/Nat/Circ.agda b/Functor/Instance/Nat/Circ.agda
index d5bcc9b..09bc495 100644
--- a/Functor/Instance/Nat/Circ.agda
+++ b/Functor/Instance/Nat/Circ.agda
@@ -2,9 +2,9 @@
 
 open import Level using (Level; _⊔_; 0ℓ)
 
-module Functor.Instance.Nat.Circ {c ℓ : Level} where
+module Functor.Instance.Nat.Circ {ℓ : Level} where
 
-open import Data.Circuit {c} {ℓ} using (Circuitₛ; mapₛ; mkCircuitₛ)
+open import Data.Circuit {ℓ} using (Circuitₛ; mapₛ; mkCircuitₛ)
 open import Data.Nat using (ℕ)
 open import Relation.Binary using (Setoid)
 open import Function using (Func)
@@ -13,20 +13,20 @@ open import Categories.Category.Instance.Setoids using (Setoids)
 open import Categories.Category.Instance.Nat using (Nat)
 open import Data.Fin using (Fin)
 open import Data.Circuit.Gate using (Gates)
-open import Functor.Instance.Nat.Edge Gates using (Edge)
-open import Functor.Instance.List using (List)
+open import Functor.Instance.Nat.Edge {ℓ} Gates using (Edge)
+open import Functor.Instance.Multiset using (Multiset)
 
-List∘Edge : Functor Nat (Setoids 0ℓ 0ℓ)
-List∘Edge = List ∘F Edge
+Multiset∘Edge : Functor Nat (Setoids ℓ ℓ)
+Multiset∘Edge = Multiset ∘F Edge
 
-module List∘Edge = Functor List∘Edge
+module Multiset∘Edge = Functor Multiset∘Edge
 
 open Func
 open Functor
 
-Circ : Functor Nat (Setoids c ℓ)
+Circ : Functor Nat (Setoids ℓ ℓ)
 Circ .F₀ = Circuitₛ
 Circ .F₁ = mapₛ
-Circ .identity = cong mkCircuitₛ List∘Edge.identity
-Circ .homomorphism = cong mkCircuitₛ List∘Edge.homomorphism
-Circ .F-resp-≈ f≗g = cong mkCircuitₛ (List∘Edge.F-resp-≈ f≗g)
+Circ .identity = cong mkCircuitₛ Multiset∘Edge.identity
+Circ .homomorphism = cong mkCircuitₛ Multiset∘Edge.homomorphism
+Circ .F-resp-≈ f≗g = cong mkCircuitₛ (Multiset∘Edge.F-resp-≈ f≗g)
diff --git a/Functor/Instance/Nat/Edge.agda b/Functor/Instance/Nat/Edge.agda
index f8d47c2..5de8f84 100644
--- a/Functor/Instance/Nat/Edge.agda
+++ b/Functor/Instance/Nat/Edge.agda
@@ -1,8 +1,9 @@
 {-# OPTIONS --without-K --safe #-}
 
 open import Data.Hypergraph.Label using (HypergraphLabel)
+open import Level using (Level; 0ℓ)
 
-module Functor.Instance.Nat.Edge (HL : HypergraphLabel) where
+module Functor.Instance.Nat.Edge {ℓ : Level} (HL : HypergraphLabel) where
 
 import Data.Vec as Vec
 import Data.Vec.Properties as VecProps
@@ -11,10 +12,9 @@ open import Categories.Category.Instance.Nat using (Nat)
 open import Categories.Category.Instance.Setoids using (Setoids)
 open import Categories.Functor using (Functor)
 open import Data.Fin using (Fin)
-open import Data.Hypergraph.Edge HL as Edge using (Edgeₛ; map; _≈_)
+open import Data.Hypergraph.Edge {ℓ} HL as Edge using (Edgeₛ; map; mapₛ; _≈_)
 open import Data.Nat using (ℕ)
-open import Data.Vec.Relation.Binary.Equality.Cast using (≈-cong′; ≈-reflexive)
-open import Level using (0ℓ)
+open import Data.Vec.Relation.Binary.Equality.Cast using (≈-reflexive)
 open import Function using (id; _∘_; Func; _⟶ₛ_)
 open import Relation.Binary using (Setoid)
 open import Relation.Binary.PropositionalEquality as ≡ using (_≡_; _≗_)
@@ -26,14 +26,6 @@ open Edge._≈_
 open Func
 open Functor
 
-Edge₁ : {n m : ℕ} → (Fin n → Fin m) → Edgeₛ n ⟶ₛ Edgeₛ m
-Edge₁ f .to = map f
-Edge₁ f .cong x≈y = record
-    { ≡arity = ≡arity x≈y
-    ; ≡label = ≡label x≈y
-    ; ≡ports = ≈-cong′ (Vec.map f) (≡ports x≈y)
-    }
-
 map-id : {v : ℕ} {e : Edge.Edge v} → map id e ≈ e
 map-id .≡arity = ≡.refl
 map-id .≡label = HL.≈-reflexive ≡.refl
@@ -59,9 +51,9 @@ map-resp-≗ f≗g .≡arity = ≡.refl
 map-resp-≗ f≗g .≡label = HL.≈-reflexive ≡.refl
 map-resp-≗ f≗g {e} .≡ports = ≈-reflexive (VecProps.map-cong f≗g (ports e))
 
-Edge : Functor Nat (Setoids 0ℓ 0ℓ)
+Edge : Functor Nat (Setoids ℓ ℓ)
 Edge .F₀ = Edgeₛ
-Edge .F₁ = Edge₁
+Edge .F₁ = mapₛ
 Edge .identity = map-id
 Edge .homomorphism = map-∘ _ _
 Edge .F-resp-≈ = map-resp-≗
diff --git a/Functor/Instance/Nat/System.agda b/Functor/Instance/Nat/System.agda
index 730f90d..00451ad 100644
--- a/Functor/Instance/Nat/System.agda
+++ b/Functor/Instance/Nat/System.agda
@@ -1,7 +1,8 @@
 {-# OPTIONS --without-K --safe #-}
 
-module Functor.Instance.Nat.System {ℓ} where
+module Functor.Instance.Nat.System where
 
+open import Level using (suc; 0ℓ)
 open import Categories.Category.Instance.Nat using (Nat)
 open import Categories.Category.Instance.Setoids using (Setoids)
 open import Categories.Functor.Core using (Functor)
@@ -9,14 +10,13 @@ open import Data.Circuit.Value using (Value)
 open import Data.Fin.Base using (Fin)
 open import Data.Nat.Base using (ℕ)
 open import Data.Product.Base using (_,_; _×_)
-open import Data.System using (System; ≤-System; Systemₛ)
+open import Data.System {suc 0ℓ} using (System; ≤-System; Systemₛ)
 open import Data.System.Values Value using (module ≋)
 open import Function.Bundles using (Func; _⟶ₛ_)
 open import Function.Base using (id; _∘_)
 open import Function.Construct.Setoid using (_∙_)
 open import Functor.Instance.Nat.Pull using (Pull₁; Pull-resp-≈)
 open import Functor.Instance.Nat.Push using (Push₁; Push-identity; Push-homomorphism; Push-resp-≈)
-open import Level using (suc)
 open import Relation.Binary.PropositionalEquality as ≡ using (_≗_)
 
 -- import Relation.Binary.Reasoning.Setoid as ≈-Reasoning
@@ -29,7 +29,7 @@ open Functor
 private
   variable A B C : ℕ
 
-map : (Fin A → Fin B) → System {ℓ} A → System B
+map : (Fin A → Fin B) → System A → System B
 map f X = record
     { S = S
     ; fₛ = fₛ ∙ Pull₁ f
@@ -88,7 +88,7 @@ System-resp-≈ {A} {B} {f = f} {g} f≗g {X} = both f≗g , both (≡.sym ∘ f
     both f≗g .≗-fₛ i s = cong fₛ (Pull-resp-≈ f≗g {i})
     both {f} {g} f≗g .≗-fₒ s = Push-resp-≈ f≗g
 
-Sys : Functor Nat (Setoids (suc ℓ) ℓ)
+Sys : Functor Nat (Setoids (suc 0ℓ) (suc 0ℓ))
 Sys .F₀ = Systemₛ
 Sys .F₁ = System₁
 Sys .identity = id-x≤x , x≤id-x
diff --git a/Functor/Monoidal/Construction/ListOf.agda b/Functor/Monoidal/Construction/ListOf.agda
index 476939e..23c6ba8 100644
--- a/Functor/Monoidal/Construction/ListOf.agda
+++ b/Functor/Monoidal/Construction/ListOf.agda
@@ -8,9 +8,9 @@ open import Categories.Functor using (Functor) renaming (_∘F_ to _∙_)
 open import Level using (Level)
 
 module Functor.Monoidal.Construction.ListOf
-    {o ℓ e : Level}
+    {o o′ ℓ ℓ′ e e′ : Level}
     {𝒞 : CocartesianCategory o ℓ e}
-    {S : MonoidalCategory o ℓ e}
+    {S : MonoidalCategory o′ ℓ′ e′}
     (let module 𝒞 = CocartesianCategory 𝒞)
     (let module S = MonoidalCategory S)
     (G : Functor 𝒞.U S.U)
diff --git a/Functor/Monoidal/Construction/MultisetOf.agda b/Functor/Monoidal/Construction/MultisetOf.agda
index 6862b84..eca7b3a 100644
--- a/Functor/Monoidal/Construction/MultisetOf.agda
+++ b/Functor/Monoidal/Construction/MultisetOf.agda
@@ -10,9 +10,9 @@ open import Category.Construction.CMonoids using (CMonoids)
 open import Level using (Level)
 
 module Functor.Monoidal.Construction.MultisetOf
-    {o ℓ e : Level}
+    {o o′ ℓ ℓ′ e e′ : Level}
     {𝒞 : CocartesianCategory o ℓ e}
-    {S : SymmetricMonoidalCategory o ℓ e}
+    {S : SymmetricMonoidalCategory o′ ℓ′ e′}
     (let module 𝒞 = CocartesianCategory 𝒞)
     (let module S = SymmetricMonoidalCategory S)
     (G : Functor 𝒞.U S.U)
diff --git a/Functor/Monoidal/Instance/Nat/System.agda b/Functor/Monoidal/Instance/Nat/System.agda
index 1b3bb34..d86588f 100644
--- a/Functor/Monoidal/Instance/Nat/System.agda
+++ b/Functor/Monoidal/Instance/Nat/System.agda
@@ -1,25 +1,25 @@
 {-# OPTIONS --without-K --safe #-}
 
-open import Level using (Level; 0ℓ; suc)
-
-module Functor.Monoidal.Instance.Nat.System {ℓ : Level} where
+module Functor.Monoidal.Instance.Nat.System where
 
 open import Function.Construct.Identity using () renaming (function to Id)
 import Function.Construct.Constant as Const
 
+open import Level using (0ℓ; suc; Level)
+
 open import Category.Monoidal.Instance.Nat using (Nat,+,0; Natop,+,0)
 open import Categories.Category.Instance.Nat using (Natop)
-open import Category.Instance.Setoids.SymmetricMonoidal {suc ℓ} {ℓ} using (Setoids-×)
+open import Category.Instance.Setoids.SymmetricMonoidal {suc 0ℓ} {suc 0ℓ} using (Setoids-×)
 open import Categories.Category.Instance.SingletonSet using (SingletonSetoid)
 open import Data.Circuit.Value using (Value)
 open import Data.Setoid using (_⇒ₛ_; ∣_∣)
-open import Data.System {ℓ} using (Systemₛ; System; ≤-System)
+open import Data.System {suc 0ℓ} using (Systemₛ; System; ≤-System)
 open import Data.System.Values Value using (Values; _≋_; module ≋)
 open import Data.Unit.Polymorphic using (⊤; tt)
 open import Data.Vec.Functional using ([])
 open import Relation.Binary using (Setoid)
 open import Relation.Binary.PropositionalEquality as ≡ using (_≡_; _≗_)
-open import Functor.Instance.Nat.System {ℓ} using (Sys; map)
+open import Functor.Instance.Nat.System using (Sys; map)
 open import Function.Base using (_∘_)
 open import Function.Bundles using (Func; _⟶ₛ_; _⟨$⟩_)
 open import Function.Construct.Setoid using (setoid)
@@ -36,12 +36,12 @@ module _ where
   discrete .fₛ = Const.function (Values 0) (SingletonSetoid ⇒ₛ SingletonSetoid) (Id SingletonSetoid)
   discrete .fₒ = Const.function SingletonSetoid (Values 0) []
 
-Sys-ε : SingletonSetoid {suc ℓ} {ℓ} ⟶ₛ Systemₛ 0
+Sys-ε : SingletonSetoid {suc 0ℓ} {suc 0ℓ} ⟶ₛ Systemₛ 0
 Sys-ε = Const.function SingletonSetoid (Systemₛ 0) discrete
 
 open import Categories.Category.Cartesian using (Cartesian)
 open import Categories.Category.Monoidal.Instance.Setoids using (Setoids-Cartesian)
-open Cartesian (Setoids-Cartesian {suc ℓ} {ℓ}) using (products)
+open Cartesian (Setoids-Cartesian {suc 0ℓ} {suc 0ℓ}) using (products)
 open import Categories.Category.BinaryProducts using (module BinaryProducts)
 open BinaryProducts products using (-×-)
 open import Categories.Functor using (_∘F_)
@@ -216,12 +216,14 @@ System-⊗-≥ {n} {n′} {m} {m′} X Y f g = record
   where
     open Cartesian (Setoids-Cartesian {0ℓ} {0ℓ}) using () renaming (products to 0ℓ-products)
     open BinaryProducts 0ℓ-products using (assocˡ)
-    open Cartesian (Setoids-Cartesian {ℓ} {ℓ}) using () renaming (products to prod)
+    open Cartesian (Setoids-Cartesian {0ℓ} {0ℓ}) using () renaming (products to prod)
     open BinaryProducts prod using () renaming (assocˡ to ×-assocˡ)
     module Pull,++,[] = SymmetricMonoidalFunctor Pull,++,[]
+    Pull,++,[]B : BraidedMonoidalFunctor
+    Pull,++,[]B = record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal }
     module Pull,++,[]B = BraidedMonoidalFunctor (record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal })
 
-    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[].braidedMonoidalFunctor using (associativity-inv)
+    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[]B using (associativity-inv)
 
     module X = System X
     module Y = System Y
@@ -238,7 +240,7 @@ System-⊗-≥ {n} {n′} {m} {m′} X Y f g = record
     ; ≗-fₒ = λ (s₁ , s₂ , s₃) → sym-++-assoc {(X.fₒ′ s₁ , Y.fₒ′ s₂) , Z.fₒ′ s₃}
     }
   where
-    open Cartesian (Setoids-Cartesian {ℓ} {ℓ}) using () renaming (products to prod)
+    open Cartesian (Setoids-Cartesian {0ℓ} {0ℓ}) using () renaming (products to prod)
     open BinaryProducts prod using () renaming (assocʳ to ×-assocʳ)
     open Cartesian (Setoids-Cartesian {0ℓ} {0ℓ}) using () renaming (products to 0ℓ-products)
     open BinaryProducts 0ℓ-products using (×-assoc; assocˡ; assocʳ)
@@ -323,7 +325,7 @@ Sys-unitaryʳ-≥ {n} X = record
     { ⇒S = < Id X.S , Const.function X.S SingletonSetoid tt >ₛ
     ; ≗-fₛ = λ i s →
         cong
-            (X.fₛ ×-⇒ Const.function (Values 0) (SingletonSetoid ⇒ₛ SingletonSetoid) (Id (SingletonSetoid {ℓ} {ℓ})) ∙ Id (Values n) ×-function ε⇒)
+            (X.fₛ ×-⇒ Const.function (Values 0) (SingletonSetoid ⇒ₛ SingletonSetoid) (Id (SingletonSetoid {suc 0ℓ} {0ℓ})) ∙ Id (Values n) ×-function ε⇒)
             sym-split-unitaryʳ
             {s , tt}
     ; ≗-fₒ = λ s → sym-++-unitaryʳ {X.fₒ′ s , tt}
@@ -371,8 +373,9 @@ Sys-braiding-compat-≤ {n} {m} X Y = record
     module X = System X
     module Y = System Y
     module Pull,++,[] = SymmetricMonoidalFunctor Pull,++,[]
-    module Pull,++,[]B = BraidedMonoidalFunctor (record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal })
-    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[].braidedMonoidalFunctor using (braiding-compat-inv)
+    Pull,++,[]B : BraidedMonoidalFunctor
+    Pull,++,[]B = record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal }
+    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[]B using (braiding-compat-inv)
     open import Categories.Functor.Monoidal.Symmetric Nat,+,0 0ℓ-Setoids-× using (module Lax)
     module Push,++,[] = Lax.SymmetricMonoidalFunctor Push,++,[]
 
@@ -389,8 +392,9 @@ Sys-braiding-compat-≥ {n} {m} X Y = record
     module X = System X
     module Y = System Y
     module Pull,++,[] = SymmetricMonoidalFunctor Pull,++,[]
-    module Pull,++,[]B = BraidedMonoidalFunctor (record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal })
-    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[].braidedMonoidalFunctor using (braiding-compat-inv)
+    Pull,++,[]B : BraidedMonoidalFunctor
+    Pull,++,[]B = record { isBraidedMonoidal = Pull,++,[].isBraidedMonoidal }
+    open import Functor.Monoidal.Braided.Strong.Properties Pull,++,[]B using (braiding-compat-inv)
     open import Categories.Functor.Monoidal.Symmetric Nat,+,0 0ℓ-Setoids-× using (module Lax)
     module Push,++,[] = Lax.SymmetricMonoidalFunctor Push,++,[]
 
-- 
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