Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis? You can read more here: Yes, that’s right. For technical reasons the n-Category Café ...

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It’s finally here: software that uses category theory to let you build models of dynamical systems! We’re going to train epidemiologists to use this to model the spread of disease. My first talk on ...

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 ...

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, ...

is always an isomorphism. The above definition is justified by the following: Theorem: A multicategory 𝒞 is isomorphic to M (𝒟) for some monoidal category 𝒟 if and only if it is representable. (we ...

Why Mathematics is Boring 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 ...

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 representation theory of the symmetric groups is clarified by thinking of all representations of all these groups as objects of a single category: the category of Schur functors. These play a ...

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

Peter Scholze has just published a challenge to the automated mathematical formalisation community in a post – Liquid tensor experiment – on Kevin Buzzard’s blog. Peter explains there the motivation ...

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 ...