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 ...

are isomorphisms. Definition. A symmetric 2-rig is a 2-rig whose underlying monoidal category is a symmetric monoidal category. One can work through the details of these definitions and show the ...

Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, ...

Of all the permutation groups, only S6 S_6 has an outer automorphism. This puts a kind of ‘wrinkle’ in the fabric of mathematics, which would be nice to explore using category theory. For starters, ...

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 ...

When sunlight falls on the light-mill the vanes turn with the black surfaces apparently being pushed away by the light. Crookes at first believed this demonstrated that light radiation pressure on the ...

Sorry - I meant terminal object for the one point space. Regarding terminology: it may not be standard, but the Aussie Cat theorists say 1-stack = sheaf 2-stack = stack a la Grothendieck and so on, ...

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 ...

where K K is the separable closure of k k, G = Gal(K | k) G = \mathrm {Gal} (K|k) is the Galois group, and we’re taking the group cohomology of G G with coefficients in the group of units K∗ K^\ast, ...

for each object X, Y, Z X, Y, Z in C \mathcal {C}. These are subject to the following conditions. The simplex category Δ \mathbf {\Delta} and its subcategory Δ⊥ \mathbf {\Delta}_ {\bot} A simple ...

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 ...

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 ...