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 ...

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 ...

Axiomatic Set Theory 1: Introduction Posted by Tom Leinster. Next: Part 2 I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using are Lawvere’s Elementary Theory ...

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 ...

and the identities as x ↦ {x} x \mapsto \{x\} gives us the Markov category FinSetMulti \mathsf{FinSetMulti} of possibilities!. The same data from the example can be used in a possibilistic way as well ...

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 ...

guest post by Wilf Offord. One of the earliest and most well-studied definitions in “higher” category theory is that of a monoidal category.

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 ...

Sure! Nominal sets are the objects of the Schanuel topos, which is the category of sheaves for a Grothendieck topology on FinSet mono op FinSet_{mono}^{op}.Whereas, the natural semantics of nullary ...