  We define a reduced $\infty$-operad $\mathcal{P}$ to be $d$-connected if the
spaces $\mathcal{P}\left(n\right)$, of $n$-ary operations, are $d$-connected
for all $n\ge0$. Let $\mathcal{P}$ and $\mathcal{Q}$ be two reduced
$\infty$-operads. We prove that if $\mathcal{P}$ is $d_{1}$-connected and
$\mathcal{Q}$ is $d_{2}$-connected, then their Boardman-Vogt tensor product
$\mathcal{P}\otimes\mathcal{Q}$ is $\left(d_{1}+d_{2}+2\right)$-connected. We
consider this to be a natural $\infty$-categorical generalization of the
classical Eckmann-Hilton argument.
