For every $n \geq 0$ there is an inclusion of the ordered set $\{0<1<\dots<n\}$ into the product $\{0<1\}^{\times n}$ sending $i$ to the increasing sequence $(0 < \dots<0<1<\dots<1)$, in which $1$ appears $i$ many times. Is there a higher analogue of this fact in n-category theory?