This dissertation studies the logic behind quantum physics, using
category theory as the principal tool and conceptual guide. To do so,
principles of quantum mechanics are modeled categorically. These
categorical quantum models are justified by an embedding into the
category of Hilbert spaces, the traditional formalism of quantum
physics. In particular, complex numbers emerge without having been
prescribed explicitly. Interpreting logic in such categories results in
orthomodular property lattices, and furthermore provides a natural
setting to consider quantifiers. Finally, topos theory, incorporating
categorical logic in a refined way, lets one study a quantum system as
if it were classical, in particular leading to a novel mathematical
notion of quantum-