Monoid homomorphisms

mh.txt

monoid homomorphism is_odd : Z -> B

Categorically, a monoid (Z, 1, (*)) is described by a pair of morphisms (const 1 : () -> Z) and (uncurry (*) : Z x Z -> Z).
A monoid homomorphism is_odd : Z -> B is a morphism which makes the following diagrams commute:

           const 1
     () ------------> Z
     |                |
  id |                | is_odd
     |                |
     v                v
     () ------------> B
         const True
                         (*)
                Z x Z ---------> Z
                  |              |
is_odd *** is_odd |              | is_odd
                  |              |
                  v              v
                B x B ---------> B
                        (&&)