By combining scientific world models and mathematical proofs we will aim to construct a ‘gatekeeper’, an AI system tasked with understanding and reducing the risks of other AI agents. In doing so ...

Announcing the Clowder Project: a wiki and reference work for category theory built using the same general infrastructure and tag system of the Stacks Project.

Why Mathematics is Boring I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

Example: suppose we have a data structure representing an abstract address. An address is, alternatively, an email address or a postal address like in the previous example. We can try to extract a ...

The notion of Cohesive Topos The definition of cohesive topos or category of cohesion aims to axiomatize properties of a topos that make it a gros topos of spaces inside of which geometry may take ...

Which properties of a type theory (for symmetric monoidal categories) make it practical? Shulman, synthesizing various observations, settles on a few basic tenets to guide the invention of the syntax ...

First I should be precise about what I mean by ‘convex body’. I simply mean a compact, convex, nonempty subset of ℝ n. (Often people include the condition that the interior is nonempty, but I’m not ...

(Jointly written by Astra Kolomatskaia and Mike Shulman) This is part two of a three part series of expository posts on our paper Displayed Type Theory and Semi-Simplicial Types. In this part, we ...