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+{-# OPTIONS --without-K --safe #-}
+
+open import Categories.Category using (Category)
+open import Categories.Category.Monoidal using (Monoidal)
+open import Categories.Category.Monoidal.Symmetric using (Symmetric)
+open import Level using (Level; _⊔_)
+
+module Category.Monoidal.Hypergraph {o ℓ e : Level} {C : Category o ℓ e} {M : Monoidal C} (S : Symmetric M) where
+
+import Categories.Category.Monoidal.Interchange.Braided as Interchange
+
+open import Categories.Category.Monoidal.Utilities M using (module Shorthands)
+open import Object.Monoid.Frobenius S using (IsSpecialCommutativeFrobeniusMonoid)
+
+open Category C
+open Symmetric S
+
+open Interchange braided using (module swapInner)
+open Shorthands using (λ⇒; λ⇐)
+open swapInner renaming (from to i⇒)
+
+record Hypergraph : Set (o ⊔ ℓ ⊔ e) where
+
+  field
+    scfm : {A : Obj} → IsSpecialCommutativeFrobeniusMonoid A
+
+  open module ISCFM {A} = IsSpecialCommutativeFrobeniusMonoid (scfm {A}) using (μ; η; δ; ϵ)
+
+  field
+    δ-compat : {X Y : Obj} → δ {X ⊗₀ Y} ≈ i⇒ ∘ δ ⊗₁ δ
+    μ-compat : {X Y : Obj} → μ {X ⊗₀ Y} ≈ μ ⊗₁ μ ∘ i⇒
+    η-compat : {X Y : Obj} → η {X ⊗₀ Y} ≈ η ⊗₁ η ∘ λ⇐
+    ϵ-compat : {X Y : Obj} → ϵ {X ⊗₀ Y} ≈ λ⇒ ∘ ϵ ⊗₁ ϵ