From: Ross Street <street@ics.mq.edu.au>
To: categories@mta.ca
Subject: Re: Limits
Date: Sun, 6 May 2001 10:26:04 +1000 [thread overview]
Message-ID: <v04210100b71a45e62755@[137.111.7.42]> (raw)
In-Reply-To: <200105042104.f44L4al17252@math-cl-n03.ucr.edu>
I very much agree with James Dolan's response to the question of
comparing categorical limits and adjoint functors with their abstract
counterparts in analysis.
Other words that have been used for "objectification" and
"categorification" are "laxification" and "identity breaking".
The original questions were a bit like asking: "Is the plus in an
abelian group a categorical coproduct?" Lots of abelian groups can
arise by taking isomorphism classes and using a categorical
coproduct: but then we lose the beautiful universal property.
Along the same lines, I enjoy bicategories, with coproducts in their
homcategories (preserved by composition), much more than additive
categories. Not only is every global coproduct in such a bicategory
also a global product, but the projections from the global products
are right adjoint to the coprojections into the coproduct.
Ross
next prev parent reply other threads:[~2001-05-06 0:26 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-05-04 21:04 Limits jdolan
2001-05-06 0:26 ` Ross Street [this message]
-- strict thread matches above, loose matches on Subject: below --
2001-05-16 22:46 Limits Paul H Palmquist
2001-05-03 23:38 Limits jdolan
2001-05-10 2:18 ` Limits Dusko Pavlovic
2001-05-02 17:02 Limits Peter Freyd
2001-05-05 18:58 ` Limits jim stasheff
2001-05-02 13:04 Limits Tobias Schroeder
2001-05-02 17:10 ` Limits Andrej Bauer
2001-05-03 12:59 ` Limits Martin Escardo
2001-05-03 23:15 ` Limits Dusko Pavlovic
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