## Universal Enveloping Algebra

"Define a coproduct $\Delta : L \rightarrow L \otimes L$ by $\Delta(x) = x \otimes 1 + 1 \otimes x$, for some $x \in L$

Show that $\Delta$ defined above is a universal enveloping algebra homomorphism."

Do I simply take $x,y \in L$, and prove that $\Delta(xy) = \Delta(x)\Delta(y)$ ??