  We define a quantum poset to be a hereditarily atomic von Neumann algebra
equipped with a quantum partial order in Weaver's sense. These quantum posets
form a category that is complete, cocomplete and symmetric monoidal closed.
This yields a quantum analogue of the inclusion order on a powerset. We show
that every quantum poset can be embedded into its powerset via a quantum
analogue of the mapping that takes each element of a poset to its down set.
