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.
Christian Williams (Feb 14 2024 at 20:02):One application of 3D string diagrams is a visual language for monoidal double categories, and similarly for monoidal fibrations.
This can be really useful for ACT; in particular the application to databases is based on regular fibrations, and so there is a powerful visual tool waiting to be made.
I made a first short post on LocalCharts. Interested to hear any thoughts.
Christian Williams (Feb 14 2024 at 22:50):I think the idea is ultimately simple, and some people ACT are well aware:
The core of the modern language of databases is the language of relations.
The basic operations of SQL, select and join, are the factors of relation composition: matching and deleting variables. These are constructed by substitution of diagonals, and pushforward of projections.
To me this just means that the basic framework for databases is given by regular categories, or more generally regular bifibrations.
[Or specifically, one with tabulation, so we can convert a relation (table) into its type of elements (rows).]
By now, CT has understood the language of relations completely, so we can bring to people both the complete and correct back-end (the type system) and the simple, intuitive front-end (the visual language).
I know some people in the community have thought a lot about similar ideas. I'm thinking of starting to write a grant; so all thoughts are more than welcome. Thanks.
Ryan Wisnesky (Feb 15 2024 at 17:39):Apparently this generalizes Spivak and Fong's graphical regular logic with e.g. first class entailments and other niceties. http://brendanfong.com/Spivak_Reglog.pdf