Re: This Week's Finds in Mathematical Physics (Week 266)

On Jun 20, 10:54 pm, b...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (John Baez)
wrote:

[...]

To set these in their proper perspective, it's good to recall
the periodic table of n-categories, mentioned in "week49":

k-tuply monoidal n-categories

n = 0 n = 1 n = 2

k = 0 sets categories 2-categories

k = 1 monoids monoidal monoidal
categories 2-categories

k = 2 commutative braided braided
monoids monoidal monoidal
categories 2-categories

[...]

Holy Christ, this stuff makes my head spin.

Not being critical, quite the reverse - it's wonderful and
awesome that so much can be constructed from such apparently
meagre axioms, but is there some prospect that, broadly
speaking, "closure" in some inductive sense will ever be
achieved with all these concepts, or will they continue
sprouting generalizations and ever higher abstractions
ad infinitum?!

Also, does anyone know if Peter Johnstone is planning a revised
(expanded?) edition of his "Sketches of an Elephant" volumes
on topos theory? I heard a rumour to that effect, and have
posponed buying the books for that reason.

(I was pleasantly surprised that Category Theory and Topos
theory wasn't as much as a pons asinorum for me as I had
feared it would be, and am quite getting into it now.)

Cheers

John Ramsden

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