Here’s my second set of lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. Part 1 is here, and ...

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 ...

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 ...

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 ...

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, ...

By the way, my proof here that the ring of symmetric functions Λ \Lambda is the free λ \lambda-ring on one generator is a bit ‘tricky’, since I was wanting to deploy things we’d already shown and not ...

Thanks for that — I had a much more complicated argument in mind, so I’m glad you came up with that simpler one. Here’s a variant on your example: splitting an idempotent is an example of a filtered ...

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 ...

guest post by Emily Pillmore and Mario Román. In functional programming, optics are a compositional representation of bidirectional data accessors provided by libraries such as Kmett’s lens, or ...

For questions 1 and 2, isn’t that true for any group G, not just the fundamental groups of a manifold? And moreover, I think of this as the definition of the profinite completion of a group: as an ...

In the previous post I set the scene a little for enriched category theory by implying that by working ‘over’ the category of sets is a bit like working ‘over’ the integers in algebra and sometimes it ...

Oh, also: there are too many posts and comments for me to keep track, so I hope this isn’t a duplicate observation. The claim that the number of cycles of lengths 1, 2, … k 1, 2, \dots k for fixed k k ...