are isomorphisms. Definition. A symmetric 2-rig is a 2-rig whose underlying monoidal category is a symmetric monoidal category. One can work through the details of these definitions and show the ...

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, ...

Of all the permutation groups, only S6 S_6 has an outer automorphism. This puts a kind of ‘wrinkle’ in the fabric of mathematics, which would be nice to explore using category theory. For starters, ...

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 ...

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 ...

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 ...

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

First, an announcement: the homotopy type theory project now has its own web site! Follow the blog there for announcements of current developments. Now, let’s pick up where we left off. The discussion ...