Abstract. Coxeter and Dynkin diagrams classify a wide variety of structures, most notably finite reflection groups, lattices having such groups as symmetries, compact simple Lie groups and complex ...

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 19, 2008 Jeffrey Morton has a paper that turns groupoids into 2-vector spaces — a key step toward constructing the Dijkgraaf–Witten model as an extended TQFT.

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 ...

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 ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

Most of us learnt as undergraduates that from an n × m n\times m-matrix M M you get two linear maps M: ℝ m → ℝ n M\colon \mathbb{R}^{m}\to \mathbb{R}^{n} and M T: ℝ n → ℝ m M^{\text{T}} \colon \mathbb ...

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 ...

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 ...

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, ...

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 ...

Last summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a ...