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 ...

Oct 12, 2007 Categorifying and q-deforming the theory of binomial coefficients — and multinomial coefficients! — using the analogy between projective geometry and set theory.

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 ...

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 learn, only to have my ...

This is the first of a series of posts on how large cardinals look in categorical set theory. My primary interest is not actually in large cardinals themselves. What I’m really interested in is ...

But for some reason I’ve never studied crossed homomorphisms, so I don’t see how they’re connected to topology… or anything else. Well, that’s not completely true. Gille and Szamuely introduce them ...

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 ...

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 ...

I want to talk about some attempts to connect the Standard Model of particle physics to the octonions. I should start out by saying I don’t have any big agenda here. It’d be great if the octonions — ...

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 ...