From: Tom Leinster <T.Leinster@dpmms.cam.ac.uk>
To: categories@mta.ca
Subject: Re: Categories ridiculously abstract
Date: Thu, 30 Nov 2000 17:30:30 +0000 (GMT) [thread overview]
Message-ID: <E141XXT-00048c-00@plover.dpmms.cam.ac.uk> (raw)
Michael Barr wrote:
>
> And here is a question: are categories more abstract or less abstract than
> sets?
A higher-dimensional category theorist's answer:
"Neither - a set is merely a 0-category, and a category a 1-category."
There's a more serious thought behind this. Sometimes I've wondered, in a
vague way, whether the much-discussed hierarchy
0-categories (sets) form a (1-)category,
(1-)categories form a 2-category,
...
has a role to play in foundations. After all, set-theorists seek to found
mathematics on the theory of 0-categories; category-theorists sometimes talk
about founding mathematics on the theory of 1-categories and providing a
(Lawverian) axiomatization of the 1-category of 0-categories; you might ask
"what next"? Axiomatize the 2-category of (1-)categories? Or the
(n+1)-category of n-categories? Could it even be, I ask with tongue in cheek
and head in clouds, that general n-categories provide a more natural
foundation than either 0-categories or 1-categories?
Tom
next reply other threads:[~2000-11-30 17:30 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-11-30 17:30 Tom Leinster [this message]
2000-12-01 22:19 ` Michael MAKKAI
2000-12-06 19:18 ` DR Mawanda
2000-12-02 13:34 ` Robert J. MacG. Dawson
-- strict thread matches above, loose matches on Subject: below --
2000-12-04 5:30 Vaughan Pratt
2000-11-29 13:39 John Duskin
2000-11-29 16:48 ` Michael Barr
2000-11-30 20:52 ` Todd Wilson
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