It’s long been a mystery why there are 3 generations of quarks and leptons: three sets of particles, apparently identical except for how they interact with the Higgs boson. It would be nice if there ...

2/18 Jacques Distler Anomaly Cancellation in Type I (part I) 2/25 Jacques Distler Anomaly Cancellation in Type I (part II) ...

Mar 19, 2007 On the category of paths whose canonical Leinster measure reproduces the path integral measure appearing in the quantization of the charged particle.

Oct 24, 2009 A Call for Comments on a Call for Papers on an issue on Mathematical Foundations of Quantum Field and Perturbative String Theory.

Mar 14, 2019 A pair of plausible-sounding and occasionally-cited claims about presentable objects are in fact false; though in practice it doesn’t matter a whole lot if we are more careful.

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 ...

The following is the greatest math talk I’ve ever watched! Etienne Ghys (with pictures and videos by Jos Leys), Knots and Dynamics, ICM Madrid 2006. [See below the fold for some links.] I wasn’t ...

This is the first of a series of posts on how large cardinals look in categorical set theory. My primary interest is not actually in large cardinals themselves. What I’m really interested in is ...

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 ...

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 ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

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 ...