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.
Josh Chen (Jan 24 2022 at 23:46):Does anyone have recommendations for good intros to higher (and possibly infinite)-dimensional rewriting systems?
John Baez (Jan 24 2022 at 23:52):I'd recommend A. Burroni’s Higher dimensional word problems and Francois Métayer's Resolutions by polygraphs for starters. Both were scooped by Ross Street's 'computads', but the French school starting with Burroni has studied a lot of examples quite nicely.
John Baez (Jan 24 2022 at 23:54):A more advanced piece of work along these lines is Métayer's Cofibrant complexes are free.
John Baez (Jan 24 2022 at 23:58):By the way, we're starting to touch on the connection between rewriting, resolutions and cofibrancy in our discussion of formal properties of the bar construction: we saw how relations in the presentation of an abelian group become the 'rewrites', aka '1-morphisms', in a 'resolution' of that group.
John Baez (Jan 24 2022 at 23:59):We haven't gone higher-dimensional yet in that discussion, but we easily could - and should.
John Baez (Jan 25 2022 at 00:02):But anyway, it's good to look at everything by Métayer, Burroni and Yves Guiruad, who has some really cool papers.
Ralph Sarkis (Jan 25 2022 at 08:15):I followed this course by Philippe Malbos and it was great. I doesn't go very high in dimensions, but it is a very good introduction.