From: "Fred E.J. Linton" <fejlinton@usa.net>
To: Tom Leinster <tl@maths.gla.ac.uk>, <categories@mta.ca>
Subject: Re: Homomorphisms that are pullbacks
Date: Mon, 02 Aug 2010 09:20:55 -0400 [thread overview]
Message-ID: <E1Og3YK-0002Xi-7p@mlist.mta.ca> (raw)
On Mon, 02 Aug 2010 08:36:21 AM EDT, Tom Leinster <tl@maths.gla.ac.uk> asked,
> Let T be a monad on some category. A map of T-algebras is a commutative
> square
>
> TA ----> TB
> | |
> | |
> V V
> A -----> B.
>
> When is this square a pullback?
One very simple instance, in Banach spaces (with norm-non-increasing
linear mappings), with T the double-dualization monad: if B is reflexive,
then such a square is a pullback iff A is reflexive, too.
The superficial similarity with the finite/discrete case of Tom's
local homeomorphism remark in the instance of compact Hausdorff spaces
may, with luck, be more than just coincidental ... (the case I mean is
that if B is a finite discrete space, then the square (in KT_2 spaces,
with T the Stone-Cech compactification monad) is a pullback iff A is
finite discrete as well).
Cheers, -- Fred
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2010-08-02 13:20 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-08-02 13:20 Fred E.J. Linton [this message]
-- strict thread matches above, loose matches on Subject: below --
2010-08-02 11:31 Tom Leinster
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