Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, ...

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: Week 26 (May 31) - The bar construction, continued.

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 E6 has 2-fold symmetry: So, this Lie group has a nontrivial outer automorphism of order 2. This corresponds to duality in octonionic projective plane geometry! There’s an ...

In Haskell notation, the example reads as follows. matchAddress :: String -> Either Address Postal buildAddress :: Postal -> Address Traversals We can go further: optics do not necessarily need to ...

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, ...

It’s now easy to get inverses: whenever you have a monoid where every element g has both a left inverse (here 1 / g) and a right inverse (here g \ 1), they must be equal, so we can take either one to ...