Author Archives: Mike Shulman

Impredicative Encodings, Part 3

In this post I will argue that, improving on previous work of Awodey-Frey-Speight, (higher) inductive types can be defined using impredicative encodings with their full dependent induction principles — in particular, eliminating into all type families without any truncation hypotheses … Continue reading

Posted in Foundations, Higher Inductive Types | 50 Comments

UF-IAS-2012 wiki archived

The wiki used for the 2012-2013 Univalent Foundations program at the Institute for Advanced Study was hosted at a provider called Wikispaces. After the program was over, the wiki was no longer used, but was kept around for historical and … Continue reading

Posted in News | 2 Comments

HoTT at JMM

At the 2018 U.S. Joint Mathematics Meetings in San Diego, there will be an AMS special session about homotopy type theory. It’s a continuation of the HoTT MRC that took place this summer, organized by some of the participants to … Continue reading

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HoTT MRC

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 | 1 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 | 13 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