  A categorical framework for modeling and analyzing systems in a broad sense
is proposed. These systems should be thought of as `machines' with inputs and
outputs, carrying some sort of signal that occurs through some notion of time.
Special cases include continuous and discrete dynamical systems (e.g. Moore
machines). Additionally, morphisms between the different types of systems allow
their translation in a common framework. A central goal is to understand the
systems that result from arbitrary interconnection of component subsystems,
possibly of different types, as well as establish conditions that ensure
totality and determinism compositionally. The fundamental categorical tools
used here include lax monoidal functors, which provide a language of
compositionality, as well as sheaf theory, which flexibly captures the crucial
notion of time.
