Extend category definition

Author: jethrolarson

readme.md

@@ -29,7 +29,7 @@ __Table of Contents__
 * [Predicate](#predicate)
 * [Contracts](#contracts)
 * [Guarded Functions](#guarded-functions)
-* [Categories](#categories)
+* [Category](#category)
 * [Value](#value)
 * [Constant](#constant)
 * [Functor](#functor)
@@ -324,9 +324,27 @@ addOne('some string') // Contract violated: expected int -> int
 
 TODO
 
-## Categories
+## Category
 
-A Category is a collection of objects (types) and functions (aka morphisms) between those types, typically sending values to values. Further, functions `a->b` and `b->c` can be composed into a new function `a->c`, the composition is associative, and there is identity function `a->a` for each object `a` that does not change functions by composing from right or from left.
+A category in category theory is a collection of objects and morphisms between them. In programming, typically types
+act as the objects and functions as morphisms. 
+
+To be a valid category 3 rules must be met:
+
+1. There must be an identity morphism that maps an object to itself.
+    Where `a` is an object in some category,
+    there must be a function from `a -> a`.
+2. Morphisms must compose.
+    Where `a`, `b`, and `c` are objects in some category,
+    and `f` is a morphism from `a -> b`, and `g` is a morphism from `b -> c`;
+    `g(f(x))` must be equivalent to `(g • f)(x)`.
+3. Composition must be associative
+    `f • (g • h)` is the same as `(f • g) * h`
+
+Since these rules govern composition at very abstract level, category theory is great at uncovering new ways of composing things.
+
+### Further reading
+* [Category Theory for Programmers](https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/)
 
 ## Value