Category Archives: Paper
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
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
Universal Properties of Truncations
Some days ago at the HoTT/UF workshop in Warsaw (which was a great event!), I have talked about functions out of truncations. I have focussed on the propositional truncation , and I want to write this blog post in case … Continue reading
Eilenberg-MacLane Spaces in HoTT
For those of you who have been waiting with bated breath to find out what happened to your favorite characters after the end of Chapter 8 of the HoTT book, there is now a new installment: Eilenberg-MacLane Spaces in Homotopy Type Theory Dan … Continue reading
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
A master thesis on homotopy type theory
In the last year, I have written my master thesis on homotopy type theory under supervision of Andrej Bauer in Ljubljana, to whom I went on an exchange, and Jaap van Oosten and Benno van den Berg in Utrecht. Their … Continue reading
Modeling Univalence in Inverse Diagrams
I have just posted the following preprint, which presents new set-theoretic models of univalence in categories of simplicial diagrams over inverse categories (or, more generally, diagrams over inverse categories starting from any existing model of univalence). The univalence axiom for … Continue reading
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
Homotopy Type Theory 