How category theory can be used to help coordinate collections of interacting large language models. Agent frameworks are popular. (These are frameworks for coordinating large language model agents, ...

Mar 11, 2026 A category-theoretic approach to “agent frameworks”: that is, frameworks for coordinating “agents” that are large language models.

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 ...

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 ...

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 ...

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 ...

I have been looking for examples, accessible to a lay audience, to illustrate the prevalence of cohomology. Here are some possibilities: ...

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 ...

In order to get used to the calculus of exact squares, the first thing we have to change is to start thinking more in terms of Kan extensions rather than limits and colimits. For instance, it’s usual ...

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