## August 16, 2019

### Graphical Regular Logic

#### Posted by John Baez

*guest post by Sophie Libkind and David Jaz Myers*

This post continues the series from the Adjoint School of Applied Category Theory 2019.

### Evil Questions About Equalizers

#### Posted by John Baez

I have a few questions about equalizers. I have my own reasons for wanting to know the answers, but I’ll admit right away that these questions are evil in the technical sense. So, investigating them requires a certain morbid curiosity… and have a feeling that some of you will be better at this than I am.

Here are the categories:

$Rex$ = [categories with finite colimits, functors preserving finite colimits]

$SMC$ = [symmetric monoidal categories, strong symmetric monoidal functors]

Both are brutally truncated stumps of very nice 2-categories!

## August 11, 2019

### Even-Dimensional Balls

#### Posted by John Baez

Some of the oddballs on the $n$-Café are interested in odd-dimensional balls, but here’s a nice thing about *even*-dimensional balls: the volume of the $2n$-dimensional ball of radius $r$ is

$\frac{(\pi r^2)^n}{n!}$

Dillon Berger pointed out that summing up over all $n$ we get

$\sum_{n=0}^\infty \frac{(\pi r^2)^n}{n!} = e^{\pi r^2}$

It looks nice. But *what does it mean?*

## August 9, 2019

### The Conway 2-Groups

#### Posted by John Baez

I recently bumped into this nice paper:

• Theo Johnson-Freyd and David Treumann, $\mathrm{H}^4(\mathrm{Co}_0,\mathbb{Z}) = \mathbb{Z}/24$.

which proves just what it says: the 4th integral cohomology of the Conway group $\mathrm{Co}_0$, in the sense of group cohomology, is $\mathbb{Z}/24$. I want to point out a few immediate consequences.

### 2020 Category Theory Conferences

#### Posted by John Baez

Here are some dates to help you plan your carbon emissions.