Split out much more structure (#37)

Monoids/Definition.agda

@@ -0,0 +1,13 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Functions
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+module Monoids.Definition where
+
+record Monoid {a : _} {A : Set a} (Zero : A) (_+_ : A → A → A) : Set a where
+  field
+    associative : (a b c : A) → a + (b + c) ≡ (a + b) + c
+    idLeft : (a : A) → Zero + a ≡ a
+    idRight : (a : A) → a + Zero ≡ a