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Morgan Rogers (he/him) (May 27 2020 at 09:46):I'm aware of (although by no means knowledgeable about) the relationship between monoids and formal languages, and through these their relation to automata: I think of these relationships as notions of "equivalent expressiveness". Petri nets seem to be a much more active topic of research in this community; I wonder if someone can tell me whether there are similar expressivity relationships between nets and other structures.
I ask because @Gershom and @sarahzrf discussed bisimulation here recently, and that relationship feels like Morita equivalence of monoids (in a way that I don't yet have the formal language to articulate :stuck_out_tongue_wink: ). I really want to apply my knowledge of monoids at some point, and if my hunch holds any water this could be a way to do that...
Fabrizio Genovese (May 27 2020 at 15:37):Well, that discussion is exactly why I creaed the new topic @Rongmin Lu refers to. I've been thrown coalgebras at, but I still fail to see how this connects with what @Gershom and @sarahzrf were talking about :slight_smile:
Gershom (May 27 2020 at 16:29):I think the one answer might be the relevant relationship "upgrades" from monoids to, well, symmetric monoidal categories -- i.e. exactly the approach the UCR group has been taking :-)