  In the topos approach to quantum theory of Doering and Isham the
Kochen-Specker Theorem, which asserts the contextual nature of quantum theory,
can be reformulated in terms of the global sections of a presheaf characterised
by the Gelfand spectrum of a commutative C*-algebra. In previous work we showed
how this topos perspective can be generalised to a class of categories
typically studied within the monoidal approach to quantum theory of Abramsky
and Coecke, and in particular how one can generalise the Gelfand spectrum. Here
we study the Gelfand spectrum presheaf for categories of quantale-valued
relations, and by considering its global sections we give a non-contextuality
result for these categories. We also show that the Gelfand spectrum comes
equipped with a topology which has a natural interpretation when thinking of
these structures as representing physical theories.
