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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...
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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...
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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...
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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...
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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). The MRC program nurtures early-career mathematicians—those who are...
View ArticleHoTT 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...
View ArticleUF-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,...
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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 —...
View ArticleHoTT 2019 Call for Submissions
Submissions of talks are now open for the International Homotopy Type Theory conference (HoTT 2019), to be held from August 12th to 17th, 2019, at Carnegie Mellon University in Pittsburgh, USA....
View ArticlePostdoctoral Position in HoTT at the University of San Diego
The University of San Diego invites applications for a postdoctoral research fellowship in homotopy type theory beginning Fall 2021, or earlier if desired. This is a two-year position with potential...
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