Author Archives: Steve Awodey

In memoriam: Vladimir Voevodsky

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HoTT awarded a MURI

We are pleased to announce that a research team based at Carnegie Mellon University has received a $7.5 million, five-year grant from the US Air Force Office of Scientific Research, as part of the highly competitive, DoD Multidisciplinary University Research Initiative … Continue reading

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The HoTT Book

This posting is the official announcement of The HoTT Book, or more formally: Homotopy Type Theory: Univalent Foundations of Mathematics The Univalent Foundations Program, Institute for Advanced Study The book is the result of an amazing collaboration between virtually everyone involved … Continue reading

Posted in Foundations, Higher Inductive Types, Homotopy Theory, Paper, Univalence | 3 Comments

HoTT Updates

Many updates have been made to the various other pages on the site: Code, Events, Links, People, References.  For example, there are several new items on models of the Univalence Axiom on the References page.

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Inductive Types in HoTT

With all the excitement about higher inductive types (e.g. here and here), it seems worthwhile to work out the theory of conventional (lower?) inductive types in HoTT. That’s what Nicola Gambino, Kristina Sojakova and I have done, as we report … Continue reading

Posted in Code, Foundations, Paper | 9 Comments

Constructive Validity

(This is intended to complement Mike Shulman’s nCat Cafe posting HoTT, II.) The Propositions-as-Types conception of Martin-Löf type theory leads to a system of logic that is different from both classical and intuitionistic logic with respect to the statements that hold … Continue reading

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Homotopy Type Theory, II | The n-Category Café

Mike Shulman has another great posting on HoTT over at the n-Cat Cafe’. It starts out like this: Homotopy Type Theory, II — Posted by Mike Shulman … Last time we talked about the correspondence between the syntax of intensional … Continue reading

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