From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: "Fred E.J. Linton" <fejlinton@usa.net>
Cc: categories <categories@mta.ca>
Subject: Re: Terminological question, and more
Date: Fri, 5 Nov 2010 09:55:57 +0000 (GMT) [thread overview]
Message-ID: <E1PEiIA-0007b6-G7@mlist.mta.ca> (raw)
In-Reply-To: <E1PEC12-0002PJ-DL@mlist.mta.ca>
On Wed, 3 Nov 2010, Fred E.J. Linton wrote:
> I've been asked for "... the name given in an arbitrary category
> to an object A for which every mono B----->A is an isomorphism."
>
> I'm stumped. Any ideas?
>
The obvious thing is to borrow a word from ordered set theory and
call it a minimal object. (All morphisms in a poset are monic.)
The term "strict initial object" is well-established for an initial
object 0 such that *every* morphism A --> 0 is an isomorphism. I've
sometimes been tempted to use "strict object" for this property
without the assumption of initiality; but the trouble is that you
then have to say "costrict object" for the dual property, which
doesn't seem right.
Peter Johnstone
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-11-05 9:55 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-11-03 21:40 Fred E.J. Linton
2010-11-05 9:55 ` Prof. Peter Johnstone [this message]
2010-11-05 11:52 ` George Janelidze
2010-11-05 12:51 ` Michael Barr
2010-11-05 23:12 Fred E.J. Linton
2010-11-10 1:23 Fred E.J. Linton
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