• select and offer are dual. They map to tag and case analysis, which are also dual: select tags the value with a label via map, synchronises via barrier, and routes to the chosen branch chain. Offer ...

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 ...

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 ...

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 ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

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 ...

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 ...

Joyal’s proof was published here: André Joyal, Une théorie combinatoire des séries formelles. Advances in Mathematics 42 (1981), 1–82. (I try not to link to Elsevier, as I’m permanently furious with ...

A Yoneda structure on a 2-category consists of two pieces of data satisfying three axioms. We will see that the data is what is necessary to naturally express the Yoneda lemma in the 2-category, and ...

Last time I took the usual construction of the quaternions from ℝ 3 \mathbb{R}^3 and modified it to construct the octonions from ℂ 3 \mathbb{C}^3. The key step was replacing the dot product on ℝ 3 ...

This looks rather like the characterization of determinant: det det is unique satisfying det (I) = 1 det(I) = 1, antisymmetry, and multilinearity. One difference is that we have symmetry rather than ...