• Kenny Courser, *Open Systems: A Double Categorical Perspective*, Ph.D. thesis, U. C. Riverside, 2020.

• John C. Baez, David Weisbart and Adam Yassine, Open systems in classical mechanics.

The basic idea is by now familiar to fans of this blog—but there are some big twists! I like treating open systems as cospans with extra structure. But in this case it makes more sense to use *spans*, since the phase space of a classical system maps *to* the phase space of any subsystem. We’ll compose these spans using pullbacks.

“Rex” means “right exact”, which is the way abelian category theorists say “preserving finite colimits”. So cognoscenti in a rush say “rex functor” for “functor preserving finite colimits”, and use “Rex” for the category of categories with finite colimits and rex functors between these. Here I’m using it for the 2-category where we include natural transformations.

The analogous term “lex” is more commonly used, since “finite limits theories” are important in categorical algebra.

This leads to the riddle:

]]>What’s the opposite of

Tyrannosaurus rex?