From 6ca9368891f8a4da36753b40efa77ef14c5efd74 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Frederik=20Hangh=C3=B8j=20Iversen?= <fhi.1990@gmail.com>
Date: Wed, 15 Nov 2017 21:51:10 +0100
Subject: [PATCH] Add the category of sets

---
 src/Category/Sets.agda | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 src/Category/Sets.agda

diff --git a/src/Category/Sets.agda b/src/Category/Sets.agda
new file mode 100644
index 0000000..fb2c332
--- /dev/null
+++ b/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 = {!!}
+    }