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, ...

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 ...

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 ...

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 ...

Things equal to the same thing are also equal to one another. And if equal things are added to equal things then the wholes are equal. And if equal things are subtracted from equal things then the ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...

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: ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

I’m in Regensburg this week attending a workshop on Interactions of Proof Assistants and Mathematics. One of the lecture series is being given by John Harrison, a Senior Principal Applied Scientist in ...

I want to talk about some attempts to connect the Standard Model of particle physics to the octonions. I should start out by saying I don’t have any big agenda here. It’d be great if the octonions — ...

There’s a dot product and cross product of vectors in 3 dimensions. But there’s also a dot product and cross product in 7 dimensions obeying a lot of the same identities! There’s nothing really like ...

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 ...