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Robin Jourde (he) (Feb 06 2026 at 15:44):Hi all,
I came across slides from a talk by Paré (Azores 2018) https://www.mscs.dal.ca/~pare/Azores.pdf about the relation between double and restriction categories and I was wondering if there were a paper related to these slides and/or more references to this story somewhere.
I know that there are DeWolf thesis which talks about double restriction categories (some sort of double categories that are restriction categories both horizontally and vertically) and the paper by Cockett and Garner Restriction categories as enriched categories explaining how restriction categories can be seen as categories enriched in some kind of double categories but I think this is not really what I am looking for.
Thanks!
Bryce Clarke (Feb 06 2026 at 16:20):There is a project in the Adjoint School 2026 which intends to investigate the connection between restriction categories and double categories.
Bryce Clarke (Feb 06 2026 at 16:21):As far as I am aware, there not any other references which develop this story further.
JS PL (he/him) (Feb 08 2026 at 09:25):I would contact Marcello Lanfranchi, I believe he has thought about these ideas (he’s discussed them with me a bit). I don’t think he’s on Zulip so here is his email: marcello.lanfranchi@mq.edu.au
Robin Jourde (he) (Feb 12 2026 at 13:19):Bryce Clarke said:
There is a project in the Adjoint School 2026 which intends to investigate the connection between restriction categories and double categories.
I know, I unfortunately forgot to register to the Adjoint school this year. I'm looking forward to the outcome of this session
Robin Jourde (he) (Feb 12 2026 at 13:26):JS PL (he/him) said:
I would contact Marcello Lanfranchi, I believe he has thought about these ideas (he’s discussed them with me a bit). I don’t think he’s on Zulip so here is his email: marcello.lanfranchi@mq.edu.au
Thanks for the recommendation! I'll reach out to him if I need to understand this more deeply
Robin Jourde (he) (Feb 12 2026 at 13:29):thank you for your answers