  This dissertation builds a compositional cyber-physical systems theory to
develop concrete semantics relating the above diverse views necessary for
safety and security assurance. In this sense, composition can take two forms.
The first is composing larger models from smaller ones within each individual
formalism of requirements, behaviors, and architectures which can be thought of
as horizontal composition -- a problem which is largely solved. The second and
main contribution of this theory is vertical composition, meaning relating or
otherwise providing verified composition across requirement, behavioral, and
architecture models and their associated algebras. In this dissertation, we
show that one possible solution to vertical composition is to use tools from
category theory. Category theory is a natural candidate for making both
horizontal and vertical composition formally explicit because it can relate,
compare, and/or unify different algebras.
