In [1], a new approach was suggested for finding quantum structures that might,
in particular, be used in potential approaches to quantum gravity
that involve non-manifold models for space and/or space-time (for example, causal sets).
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.