where F n are the Fibonacci numbers 0, 1, 1, 2, 3, … and L n are the Lucas numbers 2, 1, 3, 4, 7, …. These are two sequences satisfying the same famous recurrence relation, just with different initial ...

Jan 11, 2013 An extension of the monadicity theorem using F-categories to detect lax, pseudo, and colax morphisms provides new insight into the fundamental nature of such weak morphisms. This Week’s ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

Last time I described a way to get the Standard Model gauge group from the exceptional Jordan algebra. But that approach gave no obvious nice way to put quarks and leptons into the picture. This new ...

I don’t know much about continued fractions yet, so it’s too early to be describing historical phases of work on the subject, but I can’t resist doing it. I’ll talk about three: By thinking about ...

We start by introducing Petri nets and elementary Petri nets, which will be the focus of this post. In general, the weight of each condition can be an integer. In the case of elementary Petri nets, ...

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 ...

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 ...

You probably know that the 2010 Fields Medals have been announced. The thing is, I’ve never succeeded in understanding the slightest thing about it. It’s as if it’s got a hard, shiny shell—it resists ...

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 ...