Category

- category:

- 1. C consist of a set of object Ob(C)

- 2. for any 2 objects a b in Ob(c), exist C(a, b), a set of morphism from a to b

- 3. for all object a, there is a chosen morphism id_a in C(a, a)

- 4. for any a, b, c in Ob(c). and f :: a \rightarrow b, g :: b \rightarrow c, there is a chosen morphism g . f

- category rules:

- 1. for all morphism f, f . id = id . f = f (unital law)

- 2. for any 3 morphisms, associativity