From: Michael Barr <barr@math.mcgill.ca>
To: John Kennison <JKennison@clarku.edu>
Cc: Peter Freyd <pjf@seas.upenn.edu>,
"categories@mta.ca" <categories@mta.ca>
Subject: Re: Question on choosing subobjects consistently
Date: Sun, 29 Aug 2010 09:32:12 -0400 (EDT) [thread overview]
Message-ID: <E1OpscC-00017j-CZ@mlist.mta.ca> (raw)
In-Reply-To: <E1OpWch-0006dV-U3@mlist.mta.ca>
Here is what Grothendieck actually said (in our translation):
"Thus a subobject of $A$ is not simply an object of \C, but an
object $B$, together with a monomorphism $u:B\to A$ called the
\emph{canonical injection} of $B$ into $A$. (Nonetheless, by abuse of
language, we will often designate a subobject of $A$ by the name $B$
of the corresponding object of \C.) The containment relation defines an
\emph{order} relation (not merely a preorder relation) on the class of
subobjects of $A$. It follows from the above that the subobjects of
$A$ that are contained in a subobject $B$ are identified with the
subobjects of $B$, this correspondence respecting the natural
order."
It all depends on what he meant by "are identified with". Maybe I am
making too much of this. He regularly uses "=" for isomorphism (which I
have mostly changed in the translation).
Michael
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-08-29 13:32 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-08-28 12:24 Peter Freyd
2010-08-28 14:35 ` John Kennison
2010-08-29 13:32 ` Michael Barr [this message]
-- strict thread matches above, loose matches on Subject: below --
2010-08-26 22:09 Michael Barr
2010-08-28 10:10 ` John Kennison
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1OpscC-00017j-CZ@mlist.mta.ca \
--to=barr@math.mcgill.ca \
--cc=JKennison@clarku.edu \
--cc=categories@mta.ca \
--cc=pjf@seas.upenn.edu \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).