From: Jiri Adamek <adamek@iti.cs.tu-bs.de>
To: categories net <categories@mta.ca>
Subject: reflexive coequalizers
Date: Mon, 6 Nov 2006 14:39:47 +0100 (CET) [thread overview]
Message-ID: <E1GhFyq-0000A7-78@mailserv.mta.ca> (raw)
The indiscrete-category functor I: Set -> Cat is not algebraically
exact as I claimed in my posting of October 9. But I is
a full codomain restriction of one: as in that posting, let F
be the forgetful functor the Gabriel-Ulmer theory T
of categories to the theory of sets. Then Alg F is an algebraically
exact functor from Set to Alg T, and the Yoneda embedding
Y: Cat -> Alg T is fully faithful (since the dual of T is dense in Cat).
It is easy to see that Alg F is naturally isomorphic to Y.I , thus,
I preserves sifted colimits.
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next reply other threads:[~2006-11-06 13:39 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-11-06 13:39 Jiri Adamek [this message]
-- strict thread matches above, loose matches on Subject: below --
2006-10-09 20:09 Reflexive coequalizers Richard Garner
2006-10-09 18:40 George Janelidze
2006-10-09 14:47 Jiri Adamek
2006-10-09 10:14 Richard Garner
2006-10-09 13:37 ` Prof. Peter Johnstone
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