It’s well known that you can construct the octonions using triality. One statement of triality is that Spin ( 8) has nontrivial outer automorphisms of order 3. On the other hand, the octonions have ...

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

Feb 15, 2011 See a 4-dimensional proof of Heron’s formula for the area of a triangle. Classifying by Generalizing: The Theory of Accessibility Relative to a Limit Doctrine May 20, 2014 Summarizes “A ...

Apr 10, 2024 Symbolica is hiring category theorists. It’s already hired some, and there are job ads for 6 more. They are hiring in the UK and Australia. Verity on Descent for Strict ω-Groupoid Valued ...

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, ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

James Dolan and Chris Grossack and I had a fun conversation on Monday. We came up some ideas loosely connected to things Chris and Todd Trimble have been working on… but also connected to the ...

I have three questions. I have some guesses about the answers, so don’t think I’m completely clueless. But I’m clueless enough that I’d prefer to just give the questions, not my guesses.

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 ...