  Various frameworks that generalise the notion of contextuality in theories of
physics have been proposed; one is the sheaf-theoretic approach by Abramsky and
Brandenburger; an other is the equivalence-based approach by Spekkens. We show
that these frameworks are equivalent for scenarios with preparations and
measurements, whenever factorizability is justified. This connection gives rise
to a categorical isomorphism between suitable categories. We combine the
advantages of the two approaches to derive a canonical method for detecting
contextuality in such settings.
