(Off-topic) Question about categories

[Dominic Steinitz]

Graham,

I'm not sure if anyone mentioned the examples of a poset and a monoid as
categories. There is no "internal" structure in these. In the former, the
objects are the elements and there is a morphism between a and b iff a <= b.
A functor then becomes an order preserving map. In the latter, there is one
object and the morphisms are the elements. The identity is the identity map
and if x and y are two elements / morphisms then composition is xy. A
functor is then a homomorphism.

Dominic.