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 ...

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 ...

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 ...

This may be a tempting question when reading about categorical probability, but we might argue that this isn’t completely reinventing traditional probability from the ground up. Instead, we’re ...

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 ...

The hexagonal tiling honeycomb This picture by Roice Nelson shows a remarkable structure: the hexagonal tiling honeycomb. What is it? Roughly speaking, a honeycomb is a way of filling 3d space with ...

We then consider the problem of constructing a classifier for semi-simplicial diagrams. Specifically, we are interested in Reedy fibrant semi-simplicial diagrams, which are the homotopical counterpart ...

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 ...

One thinks of Xn as the set of n -simplices, and of the face maps as giving the boundary components of a given n -simplex. For example, X0 is the set of points, X1 is the set of lines, and X2 is the ...