One statement of triality is that textrm Spin ( 8) has nontrivial outer automorphisms of order 3. On the other hand, the octonions have nontrivial inner automorphisms of order 3. My question: can we ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

In this blog post we discuss the main (‘algebraic’) ideas of term rewriting and how they can be applied to term graph and arbitrary graph (i.e. string diagrams) rewriting. Our group was interested in ...

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 study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

String diagrams are ubiquitous in applied category theory. They originate as a graphical notation for representing terms in monoidal categories and since their origins, they have been used not just as ...

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 ...

These are notes for the talk I’m giving at the Edinburgh Category Theory Seminar this Wednesday, based on work with Joe Moeller and Todd Trimble. (No, the talk will not be recorded.) They still have ...

I’m in Regensburg this week attending a workshop on Interactions of Proof Assistants and Mathematics. One of the lecture series is being given by John Harrison, a Senior Principal Applied Scientist in ...

In the previous post I set the scene a little for enriched category theory by implying that by working ‘over’ the category of sets is a bit like working ‘over’ the integers in algebra and sometimes it ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...