First, concerning your question about monads and multiplication: a
monad on category C is exactly a monoid object in the category [C-C]
of endofunctors on C, and natural transformations between them. A
monoid in a category is, as you expect, an object X with arrows
m:X*X-X and u:1-X satisfying
G'day all.
Good day to you too.
I don't know what you mean by more complex. A dot
is just a dot, and
it has no internal structure that we can get at using
category theory
alone. Some dots may play specific roles in relation
to other dots and
arrows, but no dot is any more complex than any
