  Presheaf models provide a formulation of labelled transition systems that is
useful for, among other things, modelling concurrent computation. This paper
aims to extend such models further to represent stochastic dynamics such as
shown in quantum systems. After reviewing what presheaf models represent and
what certain operations on them mean in terms of notions such as internal and
external choices, composition of systems, and so on, I will show how to extend
those models and ideas by combining them with ideas from other
category-theoretic approaches to relational models and to stochastic processes.
It turns out that my extension yields a transitional formulation of
sheaf-theoretic structures that Abramsky and Brandenburger proposed to
characterize non-locality and contextuality. An alternative characterization of
contextuality will then be given in terms of a dynamic modal logic of the
models I put forward.
