The program for the 112th Peripatetic Seminar on Sheaves and Logic (PSSL 112) is up on the website https://sites.google.com/view/pssl112/program
17 talks on #CategoryTheory (and #TypeTheory) from a variety of speakers!

If you'd like to attend please register by March 14th following the form on the website https://sites.google.com/view/pssl112/home

@de_Jong_Tom With Ayberk's permission, I am adding a link to his PhD thesis, which includes this and more:

https://arxiv.org/abs/2603.01308

@jacobneu Good thing you're not teaching PHP!

Abstract:

I will present a constructive and predicative development of locale theory in HoTT/UF (j.w.w. Martín Escardó), with a particular focus on the theory of spectral and Stone locales. The traditional approach to the predicative development of point-free topology is to work with presentations of locales known as formal topologies. We take a different approach: we work directly with frames and locales, keeping careful track of the universes involved and adopting certain size assumptions to ensure that the theory remains amenable to predicative development. Although many fundamental constructions of locale theory appear to rely on impredicativity, these can be circumvented under rather natural size assumptions.

I will discuss the notions of spectral, regular, zero-dimensional, and Stone locales in this foundational setting, and present a predicative form of Stone duality for spectral locales: the category of large, locally small, and small-complete spectral locales (and spectral maps) is dually equivalent to the category of small distributive lattices. I will also present a predicative construction of the patch locale of a spectral locale, which allows us to exhibit Stone locales as a coreflective subcategory of spectral locales. Finally, I will discuss the point-free topology of Scott domains, whose Scott locales are always spectral. This links our development of locale theory to de Jong and Escardó's predicative development of domain theory in HoTT/UF.

The development is entirely formalized in Agda as part of Escardó's TypeTopology library: https://martinescardo.github.io/TypeTopology/Locales.index.html

This week the #HoTTEST seminar presents:

Ayberk Tosun (@ayberkt)

Constructive and predicative locale theory in univalent foundations

The talk is at 11:30am EST (16:30 UTC) on Thursday, March 5. The talk will be 60 minutes long, followed by up to 30 minutes for questions. See https://hottest-seminar.github.io/ for the Zoom link and a list of all upcoming talks.

All are welcome!

Abstract in the next post (because of the character limit)

#HoTT @carloangiuli @emilyriehl @jdchristensen

Having received multiple requests to extend the submission deadline, we are announcing a 1-week extension to the submission deadline for MFPS XLII held in Ljubljana in June.

The new extended submission deadline is March 12 (AoE).

Submission instructions and information about invited speakers and special sessions is available at https://ul-fmf.github.io/mfps-sstt-2026/.

-- Danel and Jurriaan

@mudri @dif Whoops, I accidentally copied it down wrong in my notes. Thanks for spotting this! I guess the good part is that I get to think about this all over again 🙃

@dif Fun question! I don't think you can expect a type equivalence in general. Let A be the circle with a and b both the basepoint. Then (a = b) is equivalent to the type of the integers which is a set. On the other hand, the type (Σ (P : S¹ → Set) , P base = P base) is, with univalence, equivalent to (Σ X : Set , (X ≃ X) × (X ≃ X)) and this is not a set, e.g. the elements (𝟚, id, id) and (𝟚, swap, swap) can be identified via id and via swap.

EDIT: I accidentally replaced Π by Σ, so the above is all wrong. Thanks @mudri for spotting this!

@dwarn Thanks for elaborating! I've thought about this before, but it's funny how fruitful incorrect proofs/claims tend to be for coming up with (correct proofs of) interesting results.

@MartinEscardo

@dwarn Here's a question that I can't answer: how did you come up with this?!

Now that I've finished my file, I can explain the result and why it holds, but this is relatively easy because it's post-fact. It only worked because I knew it was true and could look up critical steps in your formalization.

@MartinEscardo

@MartinEscardo @dwarn Here's my account: https://martinescardo.github.io/TypeTopology/gist.ThereAreNoHigherSemilattices2.html

My main take-away is the following observation.
A loop space is trivial if it can be equipped with a binary operation ⋆ such that
- it has an interchange law: (p ⋆ q) ∙ (r ⋆ s) ＝ (p ∙ r) ⋆ (q ∙ s);
- it is idempotent, commutative and associative.

Proving that an idempotent, commutative and associative binary operation on a pointed type induces such an operation ⋆ on its loop space is then quite tricky when it comes to commutativity and associativity. I elaborated David's argument as follows: first prove that ⋆ is commutative up to conjugation, then use idempotency to show that conjugation acts trivially, so that ⋆ really is commutative (without conjugation), and similarly (but slightly more involved) for associativity.

The intellectual credit naturally lies with David, but hopefully my elaboration/account is helpful for others too!

@jonmsterling Do you do grant proposals too? 🙃

We're happy to announce that registration for the Midlands Graduate School 2026, to take place 13–17 April at the University of Nottingham, UK, is now open:

https://ulrikbuchholtz.dk/mgs2026/

@MartinEscardo @dwarn To really understand it, I've been working on my own retelling. If I manage to complete it, I'll share it here. Thanks to both of you for sharing!

@dw Really? It seems quite reasonable to me. Definitely on the lower end of conference fees.

@OscarCunningham I don't know about the MO question, but suplattices have a prop-valued reflexive and antisymmetric relation and any type with such a relation is necessarily a set. This can be seen with a much simpler argument using what @MartinEscardo calls local Hedberg. https://martinescardo.github.io/TypeTopology/UF.HedbergApplications.html#2299

@dwarn

I am hoping to hire a postdoc, remote / hybrid possible. Timeline is: starting in next 2-6 months. If you know someone who might be a good fit and wants to work on scaling automated reasoning, static analysis, etc. (especially on modern hardware) please put them in touch with me.

Next months' PSSL looks great! https://sites.google.com/view/pssl112/program?authuser=0

I want to go...

Final call for papers for MFPS XLII.

Submission deadline is March 5! Do submit your great work!

---

MFPS XLII: Mathematical Foundations of Programming Semantics

https://ul-fmf.github.io/mfps-sstt-2026/

We are delighted to announce the 42nd Conference on the Mathematical Foundations
of Programming Semantics (MFPS XLII). It will take place at the Faculty of
Mathematics and Physics, University of Ljubljana in Ljubljana, Slovenia, from
June 1-3, 2026, where it will be colocated with the 3rd Workshop on Syntax and
Semantics of Type Theory (SSTT 2026), which is held from June 4-5, 2026.

There will be 4 invited speakers.

* Martín Escardó (University of Birmingham)
* Joost-Pieter Katoen (RWTH Aachen University)
* Cristina Matache (University of Edinburgh)
* Ana Sokolova (University of Salzburg)

There will be 2 special sessions.

* Proofs and Semantics - in celebration of Alex Simpson’s 60th birthday
(organised by Niels Voorneveld)

* Quantitative, Graded, and Interactive Semantics
(organised by Dominic Orchard)

Important dates

* Paper submission: March 5, 2026 (AoE)
* Author notification: April 23, 2026
* Conference: June 1-3, 2026

Submissions are made through EasyChair
(https://easychair.org/conferences/?conf=mfps2026).

Papers can be at most 15 pages long, excluding bibliography, and should be
prepared using the MFPS macros (https://mfpsconf.org/submissions-to-mfps/).

A preliminary version of proceedings will be distributed at the meeting. Final proceedings will be published in Electronic Notes in Theoretical Informatics and Computer Science (ENTICS, https://entics.episciences.org). This new open-access series is hosted by Episciences.org as an overlay for papers published by the CORR arXiv or HAL.

I'm on the PC of MFPS (Mathematical Foundations of Programming Semantics) this year. https://ul-fmf.github.io/mfps-sstt-2026/mfps-call-for-papers/
Please consider submitting a paper, especially if it's on constructive mathematics, domain theory, denotational semantics and/or (homotopy) type theory. MFPS will be in Ljubljana which is lovely to visit!
The submission deadline is 5 March (AoE).