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## Homework Statement

Hello,

I'd like to prove that the category cmon of commutative monoids has binary products.

## The Attempt at a Solution

actually I'm aware that i have to use cartesian products

given monoids (M, [tex]\bullet[/tex]m, [tex]e^{}_{m}[/tex]) and (N, [tex]\bullet[/tex]n, [tex]e^{}_{n}[/tex])

it follows that (M[tex]\times[/tex]N) [tex]\times[/tex] (M[tex]\times[/tex]N) [tex]\rightarrow[/tex] M[tex]\times[/tex] N

and ((m,n), (m',n')) |---> (m [tex]\bullet[/tex]m m', n [tex]\bullet[/tex]n n') ...

Thanks in advance for any help!