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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.

Posted at 8:03 AM UTC | Permalink | Followups (6)

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:

RexRex = [categories with finite colimits, functors preserving finite colimits]

SMCSMC = [symmetric monoidal categories, strong symmetric monoidal functors]

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

Posted at 7:31 AM UTC | Permalink | Followups (3)

August 11, 2019

Even-Dimensional Balls

Posted by John Baez

Some of the oddballs on the nn-Café are interested in odd-dimensional balls, but here’s a nice thing about even-dimensional balls: the volume of the 2n2n-dimensional ball of radius rr is

(πr 2) nn! \frac{(\pi r^2)^n}{n!}

Dillon Berger pointed out that summing up over all nn we get

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

It looks nice. But what does it mean?

Posted at 3:13 AM UTC | Permalink | Followups (40)

August 9, 2019

The Conway 2-Groups

Posted by John Baez

I recently bumped into this nice paper:

• Theo Johnson-Freyd and David Treumann, H 4(Co 0,)=/24\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 Co 0\mathrm{Co}_0, in the sense of group cohomology, is /24\mathbb{Z}/24. I want to point out a few immediate consequences.

Posted at 8:58 AM UTC | Permalink | Followups (14)

2020 Category Theory Conferences

Posted by John Baez

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

Posted at 7:19 AM UTC | Permalink | Post a Comment