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 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 ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

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 ...

These are notes for the talk I’m giving at the Edinburgh Category Theory Seminar this Wednesday, based on work with Joe Moeller and Todd Trimble. (No, the talk will not be recorded.) They still have ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

But for some reason I’ve never studied crossed homomorphisms, so I don’t see how they’re connected to topology… or anything else. Well, that’s not completely true. Gille and Szamuely introduce them ...

This is part two of a three part series of expository posts on our paper Displayed Type Theory and Semi-Simplicial Types. In this part, we cover the main results of the paper.

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

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 ...

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 ...