  In a recent paper by the author, a new approach was suggested for quantising
space-time, or space. This involved developing a procedure for quantising a
system whose configuration space--or history-theory analogue--is the set of
objects in a (small) category $\Q$. In the present paper, we show how this
theory can be applied to the special case when $\Q$ is a category of sets. This
includes the physically important examples where $\Q$ is a category of causal
sets, or topological spaces.
