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Benjamin Le (Jul 07 2026 at 04:51):Hi all, I'm a self-directed learner with a background in spatial puzzles and string diagrams (I'm reading Picturing Quantum Processes). I'm currently working through Schreiber's notes on cohesive HoTT, and I'm looking for a resource that develops the cohesion modalities (shape, flat, sharp) in a string-diagrammatic way (or any visual/intuitive way). Does anyone know of texts/talks that approach these modalities through diagrams first, rather than pure syntax?
My big question: Is there a visual, spatial, manipulable language for the invariants of logic itself?
(I asked a similar question on the nForum recently, but thought I'd try here as well for a broader audience. Thanks!)
John Baez (Jul 07 2026 at 08:56):I don't know one. Do these modalities obey a bunch of equations (or isomorphisms)? If so, you might be able to express those as a string diagram calculus.
Benjamin Le (Jul 07 2026 at 10:35):John Baez said:
I don't know one. Do these modalities obey a bunch of equations (or isomorphisms)? If so, you might be able to express those as a string diagram calculus.
Thanks for the direction, John. As far as I know, there are several layers of modalities - discrete, cohesive, differential, and supergeometry, with the cohesive layer being the most well-known. It has been formalized in HoTT, structured explicitly as adjunctions.
Marco Vianello (Jul 07 2026 at 10:59):Hi Benjamin, I don't have anything to add to your question at the moment, but I'd like to point you to a reading group I'm trying to put together, #learning: reading & references > Cohesive geometry study buddy. We will be working through Urs' notes (or something like that) before long, you'd be welcome to join us if you're interested
Benjamin Le (Jul 07 2026 at 14:22):Marco Vianello said:
Hi Benjamin, I don't have anything to add to your question at the moment, but I'd like to point you to a reading group I'm trying to put together, #learning: reading & references > Cohesive geometry study buddy. We will be working through Urs' notes (or something like that) before long, you'd be welcome to join us if you're interested
Thanks for the suggestion, Marco. I'll check it out.