  We provide a categorical semantics for bounded Petri nets, both in the
collective- and individual-token philosophy. In both cases, we describe the
process of bounding a net internally, by just constructing new categories of
executions of a net using comonads, and externally, using lax-monoidal-lax
functors. Our external semantics is non-local, meaning that tokens are endowed
with properties that say something about the global state of the net. We then
prove, in both cases, that the internal and external constructions are
equivalent, by using machinery built on top of the Grothendieck construction.
The individual-token case is harder, as it requires a more explicit reliance on
abstract methods.
