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 ...

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 ...

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 ...

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 ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

Monoidal Categories. Monoidal categories are categories equipped with a “product” of objects, which is associative and unital “up to isomorphism” in a specified sense.

Double limits capture the notion of limits in double categories. In ordinary category theory, a limit is the best way to construct new objects from a given collection of objects related in a certain ...

guest post by Leonardo Luis Torres Villegas and Guillaume Sabbagh. Introduction. String diagrams are ubiquitous in applied category theory. They originate as a graphical notation for representing ...

Last time I introduced a 2-dimensional complex variety called the Eisenstein surface. E = ℂ / 피 × ℂ / 피 E = \mathbb{C}/\mathbb{E} \times \mathbb{C}/\mathbb{E} . where 피 ⊂ ℂ \mathbb{E} \subset ...

The Geometric Intuition. The central motivating definition of our paper is the following: A semi-simplicial type X X consists of a type X 0 X_0 together with, for every x: X 0 x:X_0, a displayed ...

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 ...