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 ...

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 ...

A Prospectus. There are different ways to describe the relationship between type theory and set theory, but one analogy views set theory as like machine code on a specific CPU architecture, and type ...