You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
David Corfield (Jun 02 2022 at 06:51):The authors of 'Double Fibrations' write "it is well-known that aspects of logic can be encoded as fibrations of categories.... Recent investigations, however, have suggested that for some aspects of logic, double categories might be even more useful than mere categories. As such, to continue this development, a full theory of double fibrations is required."
What are these "recent investigations" likely to be?
Peter Arndt (Jun 02 2022 at 09:28):Maybe those of Christian Williams.
John Baez (Jun 02 2022 at 16:12):I don't know what those authors are thinking about, but my recent work (with many coauthors) has been using double categories of structured and decorated cospans to study Petri nets, Markov pricesses, electrical circuits, chemical reaction networks, and models of epidemiology.
John Baez (Jun 02 2022 at 16:14):And yes, my student Christian is writing his thesis about an approach to logic based on double categories. (It's interesting that he struck off on his own yet still was led to double categories.)
John Baez (Jun 02 2022 at 16:32):It took me a while to cotton on to the importance of fibrations in building double categories, but it was nicely explained by @Mike Shulman a while ago and by now it's sunk in for many of us... including in Christian's work on logic.
Morgan Rogers (he/him) (Jun 02 2022 at 20:19):David Corfield said:
The authors of 'Double Fibrations' write...
What are these "recent investigations" likely to be?
@Geoff Cruttwell and @Dorette Pronk are technically present on this Zulip, but not very active. In any case, it's always safe to ask the authors in situations like this. Drop them an email to find out from them what they meant! Worst case scenario is that they don't reply.
David Corfield (Jun 03 2022 at 08:04):John Baez said:
It took me a while to cotton on to the importance of fibrations in building double categories, but it was nicely explained by Mike Shulman a while ago and by now it's sunk in for many of us... including in Christian's work on logic.
I remember Mike explaining to us a paper on Cartesian double categories (here). This or somewhere else?