- #36

steenis

- 312

- 18

I would write that something like this

Let $y \in N = \sum_\Delta \text{ I am } h_\alpha$.

Then there are $x_\alpha \in M$ for all $\alpha \in \Delta$, such that $y = \sum_\Delta h_\alpha(x_\alpha)$.

Let $x = (x_\alpha)_\Delta$, then $x \in M^{(\Delta)}$ and $f(x) =f((x_\alpha)) = \sum_\Delta h_\alpha(x_\alpha)$ = y.

Therefore $f$ is an epimorpism.