From: Robin Adams <robin@cs.rhul.ac.uk>
To: Categories list <categories@mta.ca>
Subject: Re: question
Date: Tue, 22 Sep 2009 12:56:46 +0100 [thread overview]
Message-ID: <E1MqFlw-0007Q6-K0@mailserv.mta.ca> (raw)
On Sunday 20 September 2009 14:21:13 jim stasheff wrote:
> What do you call it when you have one (small) category being a (full)
> subcategory of another , and every object in the big category is
> isomorphic to one in the small category ? This is the case for the
> category given by objects hom(S,A) ,and morphisms given by the equivalence
> relation hom(T,A) ,as a subcategory of stack(A) .
In Adámek, Herrlich and Strecker's book "The Joy of Cats", the small category
is said to be an "isomorphism-dense" subcategory of the big category. I don't
know how widespread this terminology is, though.
> Is there an equivalence of categories ?
Yes. Whenever A is a full, isomorphism-dense subcategory of B, then the
inclusion functor from A to B is an equivalence (Remark 4.10 in that book).
--
Robin Adams <robin@cs.rhul.ac.uk>
Royal Holloway, University of London
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2009-09-22 11:56 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-09-22 11:56 Robin Adams [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-09-23 14:17 question John Kennison
2009-09-23 10:00 question Prof. Peter Johnstone
2009-09-22 12:26 question John Kennison
2009-09-22 7:04 question Fred Linton
2009-09-22 2:14 question Ross Street
2009-09-21 14:54 question Rory Lucyshyn-Wright
2009-09-20 13:21 question jim stasheff
2001-01-26 11:32 Question S.J.Vickers
2001-01-23 22:33 Question Michael J. Healy 425-865-3123
2001-01-17 0:17 Question Michael J. Healy 425-865-3123
2001-01-17 4:29 ` Question Joseph R. Kiniry
2001-01-23 5:55 ` Question Dusko Pavlovic
2000-05-31 2:08 question adrian duma
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