From: Jiri Adamek <adamek@iti.cs.tu-bs.de>
To: Gaucher Philippe <gaucher@pps.jussieu.fr>
Cc: categories@mta.ca
Subject: Re: what happens when a basic sentence is added ?
Date: Fri, 11 Feb 2011 17:36:04 +0100 (CET) [thread overview]
Message-ID: <E1PnzMS-0008RJ-08@mlist.mta.ca> (raw)
In-Reply-To: <E1PnjX5-0005HW-0M@mlist.mta.ca>
Dear Philippe,
Your question about limit theories T:
> Add a basic sentence to this theory to obtain a theory T'. So
> Mod(T') is accessible, Mod(T) is locally presentable. Is Mod(T') accessibly-
> embedded
has an affirmative answer, essentailly due to Coste's 1979 paper.
Take a cardinal k larger than the arities of the symbols of
your signature S, then both Mod(T) and Mod(T') are closed under
k-filtered colimits in Str S. (See the ananlogous argument in part II
of the proof of Theroem 5.9 of Rosicky's and mine book.) Consequently,
the embedding Mod(T') -> Mod(T) preserves k-filtered colimits.
Best regards
Jiri
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prev parent reply other threads:[~2011-02-11 16:36 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-02-10 10:59 Gaucher Philippe
2011-02-11 16:36 ` Jiri Adamek [this message]
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