Author Archives: Mike Shulman


From June 4 — 10, 2017, there will be a workshop on homotopy type theory as one of the AMS’s Mathematical Research Communities (MRCs).

Posted in News, Publicity, Uncategorized | Leave a comment

Real-cohesive homotopy type theory

Two new papers have recently appeared online: Brouwer’s fixed-point theorem in real-cohesive homotopy type theory by me, and Adjoint logic with a 2-category of modes, by Dan Licata with a bit of help from me. Both of them have fairly … Continue reading

Posted in Applications, Foundations, Paper | 12 Comments

A new class of models for the univalence axiom

First of all, in case anyone missed it, Chris Kapulkin recently wrote a guest post at the n-category cafe summarizing the current state of the art regarding “homotopy type theory as the internal language of higher categories”. I’ve just posted … Continue reading

Posted in Models, Paper, Univalence | 4 Comments

Modules for Modalities

As defined in chapter 7 of the book, a modality is an operation on types that behaves somewhat like the n-truncation. Specifically, it consists of a collection of types, called the modal ones, together with a way to turn any … Continue reading

Posted in Code, Programming | 19 Comments

Not every weakly constant function is conditionally constant

As discussed at length on the mailing list some time ago, there are several different things that one might mean by saying that a function is “constant”. Here is my preferred terminology: is constant if we have such that for … Continue reading

Posted in Univalence | 10 Comments

The HoTT Book does not define HoTT

The intent of this post is to address certain misconceptions that I’ve noticed regarding the HoTT Book and its role in relation to HoTT. (At least, I consider them misconceptions.) Overall, I think the HoTT Book project has been successful … Continue reading

Posted in Uncategorized | 6 Comments

Splitting Idempotents, II

I ended my last post about splitting idempotents with several open questions: If we have a map , a witness of idempotency , and a coherence datum , and we use them to split as in the previous post, do … Continue reading

Posted in Code, Homotopy Theory | Leave a comment