  Given a monoidal probabilistic theory -- a symmetric monoidal category
$\mathcal{C}$ of systems and processes, together with a functor $\mathbf{V}$
assigning concrete probabilistic models to objects of $\mathcal{C}$ -- we
construct a locally tomographic probabilistic theory
LT$(\mathcal{C},\mathbf{V})$ -- the locally tomographic shadow of
$(\mathcal{C},\mathbf{V})$ -- describing phenomena observable by local agents
controlling systems in $\mathcal{C}$, and able to pool information about joint
measurements made on those systems. Some globally distinct states become
locally indistinguishable in LT$(\mathcal{C},\mathbf{V})$, and we restrict the
set of processes to those that respect this indistinguishability. This
construction is investigated in some detail for real quantum theory.

Quantum Physics;Category Theory