  We propose a model-theoretic structure for Shimura varieties and give
necessary and sufficient conditions to obtain categoricity. We show that these
conditions are directly related to important conjectures in number theory
coming from Galois representations attached the points of a Shimura variety. We
end by showing that the existing literature is enough to prove categoricity of
$\mathcal{A}_{2}$ and $\mathcal{A}_{3}$.
