"Bill Page" <address@hidden> writes:
 On March 13, 2006 6:34 AM Ralf Hemmecke asked:
 > ...
 > But here the question to our category theory experts:
 > Since Monoid is something like (*,1) would it make sense
 > to speak of a category (in the mathematical sense) of
 >
 > monoids that have * and 1 as their operations
 > (1)
 >
 > ? Morphisms would respect 1 not just the identity element
 > with respect to *. And for each morphism f we would have
 > f(a*b) = f(a)*f(b). Of course as operations the two * above
 > are different but in that category they have to have the same
 > name. (No idea whether this makes sense, but it seems that
 > this is the way as "Category" it is implemented in Axiom/Aldor.)
 >
 > Then, of course, (N, +, 0) is not an object in the category
 > given by (1).
 >

 I keep trying to answer these questions but I am not sure I
 would like to classify myself as an "expert" in category theory.
 :) But here goes ...

 In category theory **Mon** (** means written in bold face font)
 consists of all monoids (as objects) and all monoid homomorphisms
 as morphisms. This does not say anything directly about what
 operation are present "inside" the objects of the category.
Agreed.