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 ...

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 ...

Thanks for a really interesting post. I hadn’t heard of Martianus Capella. Whilst Aristotle got the quantified relationship between force and velocity wrong, I happen to like his notion of force in ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

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 ordinary category theory, many results can be extended to double categories. For instance, in an ordinary category, we can determine if it has all limits (resp. finite limits) by checking if it has ...

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 ...

I’ve been talking about Grothendieck’s approach to Galois theory, but I haven’t yet touched on Brauer theory. Both of these involve separable algebras, but of different kinds. For Galois theory we ...

as you’d hope for in a categorified ring. From now on I’m going to say ‘2-rig’ when I mean symmetric 2-rig: that is, one where the tensor product is symmetric monoidal. It’s just like how algebraic ...

There are actually two questions here: who invented the concept of monoidal category, and who introduced the term ‘monoidal category’. I had always assumed both were done by Mac Lane in this paper: ...

That is correct. There are finite index subgroups of profinite groups that are not open, i.e., there are profinite groups that do not equal their own profinite completion. However, by definition, the ...

At a first glance, it seems like finding concrete definitions for these directed geometric models would be a tall order. After all, the theory of stratified cobordisms itself has its mathematical ...