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diff --git a/Algebra/Semantics.lean b/Algebra/Semantics.lean
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-import Mathlib
-import Algebra.Terms
-import Algebra.Derivations
-
-open CategoryTheory
-
-namespace NominalAlgebra
-
-section AlgebraDefinition
-
-variable (𝔸 : Type) [Infinite 𝔸] [Countable 𝔸] [DecidableEq 𝔸]
-variable (sig : Signature)
-
-structure Algebra where
-  carrier : ℕ → Nom 𝔸
-  pure (f : sig.pure) {m : ℕ} :
-    (sig.pureArgs f → carrier m) →ₑ[𝔸] carrier (m + sig.pureDepth f)
-  free (f : sig.free) {m : ℕ} :
-    (𝔸 × (sig.freeArgs f → carrier m)) →ₑ[𝔸] carrier (m + sig.freeDepth f)
-  bound (f : sig.bound) {m : ℕ} :
-    NameAbstraction 𝔸 (sig.boundArgs f → carrier m) →ₑ[𝔸] carrier (m + sig.boundDepth f)
-
-instance : CoeFun (Algebra 𝔸 sig) (fun _ => ℕ → Nom 𝔸) where
-  coe A := A.carrier
-
-@[ext]
-structure Algebra.Hom (A B : Algebra 𝔸 sig) where
-  toFun : (n : ℕ) → (A n →ₑ[𝔸] B n)
-  preserve_pure : ∀ (f : sig.pure) {m : ℕ} (args : sig.pureArgs f → A m),
-    toFun (m + sig.pureDepth f) (A.pure f args) = B.pure f (toFun m ∘ args)
-  preserve_free : ∀ (a : 𝔸) (f : sig.free) {m : ℕ} (args : sig.freeArgs f → A m),
-    toFun (m + sig.freeDepth f) (A.free f ⟨a, args⟩) = B.free f ⟨a, toFun m ∘ args⟩
-  preserve_bound : ∀ (a : 𝔸) (f : sig.bound) {m : ℕ} (args : sig.boundArgs f → A m),
-    toFun (m + sig.boundDepth f) (A.bound f (⟪a⟫ args)) = B.bound f (⟪a⟫ toFun m ∘ args)
-
-instance {A B : Algebra 𝔸 sig} : CoeFun (Algebra.Hom 𝔸 sig A B) (fun _ => (n : ℕ) → (A n →ₑ[𝔸] B n)) where
-  coe h := h.toFun
-
-end AlgebraDefinition
-
-section Algebra
-
-variable {𝔸 : Type} [Infinite 𝔸] [Countable 𝔸] [DecidableEq 𝔸]
-variable {sig : Signature}
-
-namespace Algebra
-
-def Hom.id (A : Algebra 𝔸 sig) : Hom 𝔸 sig A A where
-  toFun _ := EquivariantMap.id 𝔸
-  preserve_pure _ _ _ := rfl
-  preserve_free _ _ _ _ := rfl
-  preserve_bound _ _ _ _ := rfl
-
-def Hom.comp {A B C : Algebra 𝔸 sig} (h : Hom 𝔸 sig B C) (g : Hom 𝔸 sig A B) : Hom 𝔸 sig A C where
-  toFun n := EquivariantMap.comp 𝔸 (h n) (g n)
-  preserve_pure f m args := by
-    rw [EquivariantMap.comp_app, g.preserve_pure, h.preserve_pure]
-    rfl
-  preserve_free a f m args := by
-    rw [EquivariantMap.comp_app, g.preserve_free, h.preserve_free]
-    rfl
-  preserve_bound a f m args := by
-    rw [EquivariantMap.comp_app, g.preserve_bound, h.preserve_bound]
-    rfl
-
-instance : Category (Algebra 𝔸 sig) where
-  Hom := Hom 𝔸 sig
-  id := Hom.id
-  comp h g := Hom.comp g h
-
-def forgetfulFunctor : Algebra 𝔸 sig ⥤ Nom 𝔸 where
-  obj X := X 0
-  map f := f.toFun 0
-
-end Algebra
-
-end Algebra
-
-end NominalAlgebra