Oh, and I forgot, but many many thanks to @fnf and all the locals for making it happen, you nailed it ❤️

This is your yearly reminder that anyone who publishes CS papers should have a personal website that lists their current position, research interests, publications, and email address.

If you don't, it's basically impossible for me to invite you to a PC, invite you to give a talk, ask a question about your work, or recommend you to others when asked.

slides for my TYPES 2025 talk, "a guided tour of polarity and focusing", are available here:

https://chrisamaphone.hyperkind.org/types-2025.html

it was recorded, but the recording may not be up for awhile. if you have questions about anything on the slides in the meantime, let me know!

@oantolin

Small side-remark: any type with decidable equality is an hset (by Hedberg's theorem).

Yesterday, I gave a talk at TYPES in Glasgow on my work with @MartinEscardo on predicative Stone duality for spectral locales in univalent foundations.

The slides for the talk are available here: https://msp.cis.strath.ac.uk/types2025/slides/TYPES2025-slides82.pdf

In our previous work [1] on the predicative treatment of the patch locale (j.w.w. @IgorArrieta), we proposed a predicatively well-behaved definition of spectrality. This can be found on slide 16 of this presentation.

In this work, we formally establish that this definition of spectrality is correct in the sense that these are exactly the locales defined by the frames of (small) ideals over (small) distributive lattices.

This is thanks to Condition (SP4) which says something quite strong: the type of compact opens of the locale in consideration has a specified, small copy. Despite its strength, however, this condition is a proposition, and this seems to be possible thanks to univalence.

[1]: https://arxiv.org/abs/2402.03134

@ecavallo @MartinEscardo

Thanks Evan! This is quite interesting especially because I'd like to generalize injectivity from types to maps and get an algebraic wfs.

TYPES talk done! Time to enjoy the rest of the conference 😄 I talked about injective types in univalent mathematics which is joint work with @MartinEscardo. You can find my slides here https://tdejong.com/talks/TYPES-2025.pdf.

#TYPES2025 #typetheory #HoTT

PhD defense passed :)

@fnf @chrisamaphone Ran 16.05 last night 😄 But I'd be up for slower/easier runs while at TYPES!

Taking "algebraically" seriously in the definition of algebraically injective type.

In this thread, I want to discuss recent developments regarding the notion of algebraically injective type that I discussed in the following paper:

Injective types in univalent mathematics
https://doi.org/10.1017/S0960129520000225

I gave a talk today about this at the ASSUME seminar:

Taking “algebraically” seriously in the definition of algebraically injective types
https://tdejong.com/ASSUME/

If you don't want to read this thread, you can jump directly to the slides:
https://martinescardo.github.io/.talks/2025-05-29-Note-09-58-algebraic-injectives-assume_pdf.pdf

1/

https://arxiv.org/abs/2506.02759

Something on the arXiv from Christian Sattler and I today!

This paper is about small object arguments, which are used in homotopy theory to construct various factorizations of maps. A little more specifically, it's about Garner's *algebraic* small object argument, which is a more recent, more general, more frequently constructive variant of the original argument (due to Quillen). We start from a certain useful characterization of factorizations coming with Quillen's argument and hunt down an analogue of sorts for the algebraic case.

I hope the paper will be interesting to people who are interested in these things in general, but of course for me the motivation is in semantics of homotopy type theory. The algebraic small object argument is used in particular in the cubical model constructions, and the reason we ended up writing this paper is because we needed the result somewhere deep in an argument about these models. Someday you'll hear more about that :)

I talked about this work at HoTT/UF a month and a half ago, so you can check out some slides and video at https://hott-uf.github.io/2025/

@mevenlennonbertrand With that many academics, I'm sure there's at least one (but not me!)

Happy to see the second paper of our PhD student @Stiephen Pradal on the arXiv today! 😄
https://arxiv.org/abs/2506.01717

He continues the study of the fat Delta category — a modification of the simplex category introduced by Joachim Kock — and gives a presentation by generators and relations.

Today I'm feeling very demoralised because yet another grant proposal I spent many hours working on was rejected. I've submitted 8 grant proposals total in my career, and 7 have been rejected. One I'm still waiting about. I've published repeatedly in top conferences, I've submitted for industry and government grants, I've submitted both alone and with collaborators from both industry and academia. I've had academics and external outside opinion review of my proposals and all feedback I've ever gotten on them have always been positive. It's just extremely demoralising, and makes me want to quit academia and become a monk or something.

🚨 #ESSLLI2025 - Last chance for early bird registration (May 31)!
👉 Logic
👉 Language
👉 Information
Really interesting courses and the Ruhr area is much more interesting than it is known for! ✨
#nlproc #logic #linguistics #summerschool
https://2025.esslli.eu/registration.html

An updated of version of the Yoneda paper has appeared on the arxiv (https://arxiv.org/abs/2501.13229). Featuring: tidier proofs, a simpler axiom, and various other improvements.

This is nominally the technical report to the LICS paper, but we've attempted to merely extend the exposition in that paper with more details (rather than just include a list of proofs). Hopefully this version is therefore a compromise between detail and readability!

Last couple of days before the final registration deadline: https://msp.cis.strath.ac.uk/types2025/

On the first of several trains to CIRM for this nice workshop on semantics of programming languages 😄 https://conferences.cirm-math.fr/3518.html

@olynch Maybe (not sure) you're also interested in the work by @noamzoam and @pamellies

- Noam's OPLSS 2016 / MGS 2019 notes
(https://www.noamz.org/oplss16/refinements-notes.pdf)
- Functors are Type Refinement Systems (https://doi.org/10.1145/2676726.2676970)
- Type refinement and monoidal closed bifibrations (https://arxiv.org/abs/1310.0263)

For those interested in a principled approach to probability and the underlying mathematics & logic, a new version of my book is online:

http://www.cs.ru.nl/B.Jacobs/PAPERS/ProbabilisticReasoning.pdf

This 1000 page book presents a fresh perspective and a new language, as part of a new emerging field "Categorical Probability Theory", with many examples.

Three chapters have been added, on learning from multiple data, on causality, and on probabilistic automata.

One more chapter to go, on continuous probability.

Feedback is welcome