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From: Tom Leinster <leinster@ihes.fr>
To: categories@mta.ca
Subject: Re: Compatibility of functors with limits
Date: Sun, 20 Jul 2003 19:50:35 +0200 (CEST)	[thread overview]
Message-ID: <Pine.LNX.4.44.0307201945550.24042-100000@ssh.ihes.fr> (raw)

Mamuka Jibladze wrote:

> A related question: does anybody know any analogs of the
> Freyd's Adjoint Functor Theorems for functors between
> in(co)complete categories?

Borceux states the 'More General Adjoint Functor Theorem' in Vol 1, 6.6.1
of his Handbook.  This requires only that the codomain of the hoped-for
left adjoint is Cauchy-complete (and of course that the known functor has
some properties: it is 'absolutely flat' and satisfies some solution set
conditions).

Here's a representability theorem, presumably related.  Let C be a small,
Cauchy-complete category and let X: C ---> Set.  Then

   X is representable  <=>  X respects small limits.

The same goes for familial representability and connected limits.  Proofs
are at

   http://www.ihes.fr/~leinster/rr.ps

Tom













             reply	other threads:[~2003-07-20 17:50 UTC|newest]

Thread overview: 5+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2003-07-20 17:50 Tom Leinster [this message]
     [not found] <Pine.LNX.3.96.1030716154419.29520A-100000@plover.dpmms.cam.ac.uk>
2003-07-16 14:58 ` Tom LEINSTER
  -- strict thread matches above, loose matches on Subject: below --
2003-07-13 17:34 Tom LEINSTER
2003-07-15 14:48 ` Mamuka Jibladze
2003-07-04 17:05 leinster

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