# Commutative monoids have binary products

imlala

## 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, $$\bullet$$m, $$e^{}_{m}$$) and (N, $$\bullet$$n, $$e^{}_{n}$$)

it follows that (M$$\times$$N) $$\times$$ (M$$\times$$N) $$\rightarrow$$ M$$\times$$ N

and ((m,n), (m',n')) |---> (m $$\bullet$$m m', n $$\bullet$$n n') ....

Thanks in advance for any help!

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