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 ...

Jun 1, 2007 Three approaches to connections and gauge transformations, leading up to one based on Toby Bartels’ notion of “smooth anafunctor”.

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 ...

I move jobs tomorrow: from Glasgow to Edinburgh, city of James Clerk Maxwell, Arthur Conan Doyle, Robert Louis Stevenson and Dolly the Sheep. But before I go, I want to give you the fourth and final ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

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 ...

Before we go any further, let’s replace topological spaces with their open-set lattices. (For suitably nice topological spaces, this doesn’t lose any information.) This is a good idea since lattices ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

Elaine Landry, in the philosophy department at U. C. Davis, is putting together a book called Categories for the Working Philosopher. Here are the contributors and their (perhaps tentative) topics: I ...