These are some lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I ...

and indeed addition and the Cauchy product give the category of species a structure much like that of a ring! It’s even more like a ‘rig’, which is a ‘rings without negatives’, since we can add and ...

At the Topos Institute this summer, a group of folks started talking about thermodynamics and category theory. It probably started because Spencer Breiner and my former student Joe Moeller, both ...

Guest post by John Wiltshire-Gordon. My new paper arXiv:1508.04107 contains a definition that may be of interest to category theorists. Emily Riehl has graciously offered me this chance to explain. In ...

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, ...

Some trivial examples of nonperiodic discretely-supported measures with discretely-supported Fourier transforms: since the fourier transform of any lattice-counting measure is essentially a dual ...

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 you’ve ...

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 ...

The monoid of n × n n \times n matrices has an obvious n n-dimensional representation, and you can get all its representations from this one by operations that you can apply to any representation. So ...

I think I’ve seen Bayesians say that same thing on the other side of the isomorphism ℝ ≅ (0, ∞) \mathbb{R}\cong (0,\infty).That is, if you take the logarithms of the prior probability and the ...

As Valeria de Paiva mentioned, this is possible by considering a slightly different definition of the Dialectica category. Objects in the original definition are (equivalence classes of) monos into ...

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 ...