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 ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

Summer saw the foundations of mathematics rocked by the publication of The HoTT Book. Here we are a few months later and the same has happened to physics with the appearance on the ArXiv of Urs’s ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Most of us learnt as undergraduates that from an n × m n\times m-matrix M M you get two linear maps M: ℝ m → ℝ n M\colon \mathbb{R}^{m}\to \mathbb{R}^{n} and M T: ℝ n → ℝ m M^{\text{T}} \colon \mathbb ...