From: dusko <dusko@kestrel.edu>
To: Categories <categories@mta.ca>
Subject: Re: cracks and pots
Date: Tue, 28 Mar 2006 00:01:38 -0800 [thread overview]
Message-ID: <CB9F540D-DE8F-4C42-B0A1-7EA8BF81E155@kestrel.edu> (raw)
i think david yetter's analysis of the dichotomy "categories as
foundations" vs "categories as algebra" was spot on --- with respect
to people and the community. indeed, one could split most of our
papers into one category or the other.
but at the end of the day, i think, we'll all agree that the source
of the unreasonable effectiveness of categorical algebra is its
foundational content (although there is probably a lot of it that we
dont understand yet); and the other way around. eg, if you look at
grothendieck's work, he started working in algebra, and ended up
developing foundational structures, because he needed them. and a lot
on the "algebra" side now is built upon them. ok, then for a while it
was thought that he exaggerated with foundations, and that a more
direct approach "could have been in better taste" (to cite
eilenberg). but maby the fermat theorem would have a more useful
proof if it was developed in grothendieck style. and nowadays, there
is a lot of foundational content in tannaka duality etc, in TQFT in
general, but we only see hints of it at the moment (and i for one
just see the reflections of these hints in other people's eyes).
i am of course saying things very clear and familiar to many people
on this list, but maby they are worth saying nevertheless. it might
be good if the links between "categories as algebras" and "categories
as foundations" would not boil down just to the greatest of the
category theorists, leaving the rest of us in two camps.
-- dusko
next reply other threads:[~2006-03-28 8:01 UTC|newest]
Thread overview: 43+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-03-28 8:01 dusko [this message]
2006-03-29 12:57 ` Alex Simpson
-- strict thread matches above, loose matches on Subject: below --
2006-03-29 19:23 dusko
2006-03-29 14:02 David Yetter
2006-03-26 13:37 V. Schmitt
2006-03-25 3:22 David Yetter
2006-03-24 16:24 Marta Bunge
2006-03-23 19:45 Peter Arndt
2006-03-23 16:50 Eduardo Dubuc
2006-03-26 13:25 ` Urs Schreiber
2006-03-19 18:25 Steve Vickers
2006-03-18 15:19 James Stasheff
2006-03-17 18:29 Robert J. MacG. Dawson
2006-03-17 17:26 Eduardo Dubuc
2006-03-17 16:24 Krzysztof Worytkiewicz
2006-03-17 14:25 jim stasheff
2006-03-17 9:36 George Janelidze
2006-03-17 8:49 Marta Bunge
2006-03-17 8:06 Marta Bunge
2006-03-17 1:52 Vaughan Pratt
2006-03-18 15:21 ` James Stasheff
2006-03-18 20:22 ` Mamuka Jibladze
2006-03-16 20:47 John Baez
2006-03-16 18:41 Robert J. MacG. Dawson
2006-03-16 17:29 Eduardo Dubuc
2006-03-16 14:54 Robert J. MacG. Dawson
2006-03-16 12:05 dusko
2006-03-16 9:51 V. Schmitt
2006-03-15 21:00 Eduardo Dubuc
2006-03-15 13:35 RFC Walters
2006-03-14 19:56 John Baez
2006-03-15 12:23 ` Marta Bunge
2006-03-15 17:26 ` Krzysztof Worytkiewicz
[not found] <BAY114-F26C035E683A780D5555217DFE10@phx.gbl>
2006-03-14 17:08 ` Robert J. MacG. Dawson
2006-03-14 17:48 ` Marta Bunge
2006-03-27 14:28 ` Peter Selinger
2006-03-12 22:29 Marta Bunge
2006-03-14 6:08 ` David Yetter
2006-03-14 23:18 ` Robert Seely
2006-03-14 14:55 ` Eduardo Dubuc
2006-03-14 16:05 ` Robert J. MacG. Dawson
2006-03-14 16:30 ` Marta Bunge
2006-03-14 23:26 ` Dominic Hughes
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