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, ...

guest post by Sarah Griffith and Jade Master. Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional ...

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 ...

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 ...

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 ...

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 ...

Sure! Nominal sets are the objects of the Schanuel topos, which is the category of sheaves for a Grothendieck topology on FinSet mono op FinSet_{mono}^{op}.Whereas, the natural semantics of nullary ...