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 ...

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 ...

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 ...

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 ...

In Haskell notation, the example reads as follows. matchAddress :: String -> Either Address Postal buildAddress :: Postal -> Address Traversals We can go further: optics do not necessarily need 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, ...

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 ...

Yes, both sets of co-authors should be corrected. The pyknotic team is Clark Barwick and Peter Haine. The condensed team is Dustin Clausen and Peter Scholze. There’s some relation with the ...

The “sentence space” F(s) F (s) is taken to be a one dimensional space in which 0 0 corresponds to false and the basis vector 1S 1_S corresponds to true. As before, transitive verbs have type nrsnl ...

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 ...