From: Jiri Rosicky <rosicky@math.muni.cz>
To: cat-dist@mta.ca
Subject: re: question about lambda-filtered colimits
Date: Tue, 2 Dec 2003 16:42:02 +0100 [thread overview]
Message-ID: <20031202154202.GA19936@queen.math.muni.cz> (raw)
The proof can be found in the paper
J.Adamek, H.Herrlich, J.Rosicky, W.Tholen, On a generalized small-object
argument for the injective subcategory problem, Cah. Top. Geom. Diff.
Cat. XLIII (2002), 83-106.
----- Forwarded message from Gaucher Philippe <gaucher@pps.jussieu.fr> -----
>
>
> Dear category theorists
>
>
> I would be interested in knowing a proof of the following fact (due to J.
> Smith):
>
> "In a combinatorial model category M (i.e. a locally presentable cofibrantly
> generated model category), there are functorial factorizations of a map into
> a trivial cofibration followed by a fibration which preserve lambda-filtered
> colimits for sufficiently large regular cardinals lambda. The same is true
> for the factorizations as a cofibration followed by a trivial fibration."
>
> As far as I know about the proof, it suffices to apply the small object
> argument step-by-step and then to use some property of lambda-filtered
> colimits. The only property I know close to the problem is that a
> lambda-filtered colimits of lambda-presentable objects is lambda-presentable.
> But the underlying diagram of a pushout is not lambda-filtered. So I dont
> understand...
>
> Thanks in advance. pg.
>
>
>
>
----- End forwarded message -----
next reply other threads:[~2003-12-02 15:42 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-12-02 15:42 Jiri Rosicky [this message]
-- strict thread matches above, loose matches on Subject: below --
2003-12-01 12:45 Gaucher Philippe
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