Forgot to add monoid-module

src/Cat/Category/Monoid.agda

@@ -0,0 +1,45 @@
+module Cat.Category.Monoid where
+
+open import Agda.Primitive
+
+open import Cat.Category
+open import Cat.Category.Product
+open import Cat.Category.Functor
+import Cat.Categories.Cat as Cat
+
+-- TODO: Incorrect!
+module _ (ℓa ℓb : Level) where
+  private
+    ℓ = lsuc (ℓa ⊔ ℓb)
+
+  -- Might not need this to be able to form products of categories!
+  postulate unprovable : IsCategory (Cat.RawCat ℓa ℓb)
+
+  open HasProducts (Cat.hasProducts unprovable)
+
+  record RawMonoidalCategory : Set ℓ where
+    field
+      category : Category ℓa ℓb
+    open Category category public
+    field
+      {{hasProducts}} : HasProducts category
+      mempty  : Object
+      -- aka. tensor product, monoidal product.
+      mappend : Functor (category × category) category
+
+  record MonoidalCategory : Set ℓ where
+    field
+      raw : RawMonoidalCategory
+    open RawMonoidalCategory raw public
+
+module _ {ℓa ℓb : Level} (ℂ : MonoidalCategory ℓa ℓb) where
+  private
+    ℓ = ℓa ⊔ ℓb
+
+  module MC = MonoidalCategory ℂ
+  open HasProducts MC.hasProducts
+  record Monoid : Set ℓ where
+    field
+      carrier : MC.Object
+      mempty  : MC.Arrow (carrier × carrier)  carrier
+      mappend : MC.Arrow MC.mempty carrier