Add the category of sets

src/Category/Sets.agda

@@ -0,0 +1,34 @@
+module Category.Sets where
+
+open import Cubical.PathPrelude
+open import Agda.Primitive
+open import Category
+
+-- Sets are built-in to Agda. The set of all small sets is called Set.
+
+Fun : {ℓ : Level} → ( T U : Set ℓ ) → Set ℓ
+Fun T U = T → U
+
+Sets : {ℓ : Level} → Category {lsuc ℓ} {ℓ}
+Sets {ℓ} = record
+  { Object = Set ℓ
+  ; Arrow = λ T U → Fun {ℓ} T U
+  ; 𝟙 = λ x → x
+  ; _⊕_  = λ g f x → g ( f x )
+  ; assoc = refl
+  ; ident = funExt (λ x → refl) , funExt (λ x → refl)
+  }
+
+module _ {ℓ ℓ' : Level} {ℂ : Category {ℓ} {ℓ}} where
+  private
+    C-Obj = Object ℂ
+    _+_   = Arrow ℂ
+
+  RepFunctor : Functor ℂ Sets
+  RepFunctor =
+    record
+    { F = λ A → (B : C-Obj) → Hom {ℂ = ℂ} A B
+    ; f = λ { {c' = c'} f g → {!HomFromArrow {ℂ = } c' g!}}
+    ; ident = {!!}
+    ; distrib = {!!}
+    }