ItaCa Folk Ensemble

Category theory is full of “hidden gems”, which means interesting papers that are written in obscure or obsolete language, where there are no diagrams, and proofs are often just sketched.

This is unpleasant for various reasons: it takes a toll on young students, it prevents ideas from circulating easily, it relegates instructive papers (often, filled with ground-breaking ideas that we discovered/refined later!) to oblivion.

We believe that a good service to the community of category theorists around the world would be to make these resources more popular, more accessible, well typeset, and expanded. In spirit, this intersects some of the motivations for Jon Sterling’s mathematical translations project.

Hence our desire to involve young students in a small project of literature review, translation and outreach. The ultimate goal of the project is to produce a manuscript of some sort expanding, completing and renovating a few hidden gems.

This is a call for students!

Anyone who is interested can contact the two people that (so far) are responsible of the project:

• Fosco Loregian
• Ivan Di Liberti

(you can contact us also in case you want to become a “mentor”!).

Updates on the project

🎓 In March 2023 Guido Boccali, Andrea Laretto, Fosco Loregian, Stefano Luneia wrote the preprints Bicategories of automata, automata in bicategories and Completeness for categories of generalized automata.

🎉 In May 2023 Completeness for categories of generalized automata was accepted by CALCO2023 as a ‘coalgebraic pearl’. Kudos to Guido, Stefano and Andrea!

🎓 In May 2023 the same group, together with Bojana Femić, wrote the preprint The semibicategory of Moore automata.

We are currently working hard on:

• use bicategories to describe the Krohn-Rhodes theorem;
• use bicategories to describe bi-similarity and the colgebraic approach to automaton categories;
• use intuition from automata theory to describe actions of categories and not only of monoids;
• use bicategories to collect classes of state machines in solid and manageable mathematical structures.

The door of ItaCa Folk Ensemble is always open: if you feel like you want to join the ongoing projects, or propose a new one, contact us!