Note: These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older ...

At the Topos Institute this summer, a group of folks started talking about thermodynamics and category theory. It probably started because Spencer Breiner and my former student Joe Moeller, both ...

This week in our seminar on Cohomology and Computation we continued discussing the bar construction, and drew some pictures of a classic example ...

The math-blogosphere is abuzz with interest in the new Math Overflow, a mathematics questions and answers site. Already we at the Café have been helped with the answer to a query on the Fourier ...

Category Theory and Biology Posted by David Corfield Some of us at the Centre for Reasoning here in Kent are thinking about joining forces with a bioinformatics group. Over the years I’ve caught ...

If you missed the earlier parts of this series, you can see polished-up versions on my website: Part 1: integral octonions and the Coxeter group E 10. Also available here on the n -Category Café .

Let’s take a break from all this type theory and ∞ \infty-stuff and do some good old 2-dimensional category theory. Although as usual, I want to convince you that plain old 2-categories aren’t good ...

The Dynkin diagram of E 6 \mathrm{E}_6 has 2-fold symmetry: Today I want to tell you about invariant structures on the exceptional Jordan algebra and its dual. But a lot of this stuff applies more ...

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 ...

The history This paper got its start in April 2007 when Allen Knutson raised a question about Schur functors here on the n n -Category Café. I conjectured an answer, and later Todd Trimble refined the ...

Part of what intrigues me about reading Terence Tao’s blog is that he displays there a different aesthetic to the one largely admired here. The best effort to capture this difference is, I believe, ...

Maybe people who are all excited about the “field with one element” should start at the beginning and think a bit about the “group with no elements”.