Category theory studies the composition of (things that look like) functions. So each thing has a domain, and a codomain, and if we compose A --f--> B with B --

Category theory studies the composition of (things that look like) functions. So each thing has a domain, and a codomain, and if we compose A --f--> B with B --g--> C then the intermediate B goes away. This doesn't sit nicely with how parallel composition works, e.g. If I talk to Google, that doesn't prevent you from talking to Google. That's the essence of why category theory works nicely with pure functional programming, but beyond that simply fails to be useful. In particular, there has been virtually no progress in useful categorical models of parallel computation.