  This note concerns the category $\Box$ of cartesian cubes with connections,
equivalently the full subcategory of posets on objects $[1]^n$ with $n \geq 0$.
We show that the idempotent completion of $\Box$ consists of finite complete
posets. It follows that cubical sets, ie presheaves over $\Box$, are equivalent
to presheaves over finite complete posets. This yields an alternative
exposition of a result by Kapulkin and Voevodsky that simplicial sets form a
subtopos of cubical sets.
