From: Richard Garner <richard.garner@mq.edu.au>
To: Emily Riehl <eriehl@math.harvard.edu>
Cc: Categories list <categories@mta.ca>
Subject: Re: orthogonal factorization systems
Date: Sun, 15 Apr 2012 08:27:57 +1000 [thread overview]
Message-ID: <E1SJP2X-0000QA-8H@mlist.mta.ca> (raw)
In-Reply-To: <E1SJ2wO-0004lQ-E6@mlist.mta.ca>
Dear Emily,
You are in luck. Your result is an instance of the following:
PROP
If C is a category bearing the orthogonal factorisation system (E,M),
and T is a monad on C whose underlying functor preserves E-maps, then
C^T bears the orthogonal factorisation system (U^-1(E), U^-1(M)).
A full proof of which is given as Proposition 20.28 in:
Abstract and concrete categories: The joy of cats (Wiley, 1990)
Jiri Adamek, Horst Herrlich and George Strecker
Maybe there is an older reference than this but I am not aware of such.
Richard
On 14 April 2012 08:09, Emily Riehl <eriehl@math.harvard.edu> wrote:
> I've placed a bet with a colleague that the following result appears in
> the literature. Please help me win.
>
> Claim: Suppose (E,M) is an orthogonal factorization system (unique lifts)
> on a symmetric monoidal category and X is a fixed monoid. If tensoring
> with X preserves maps in the class E, then (E,M) lifts to an orthogonal
> factorizaiton system on the category of X-modules.
>
> Regards,
> Emily Riehl
>
>
>
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2012-04-14 22:27 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-04-13 22:09 Emily Riehl
2012-04-14 22:27 ` Richard Garner [this message]
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