* regular monos not closed under composition
@ 2006-05-16 20:20 Thomas Streicher
0 siblings, 0 replies; 2+ messages in thread
From: Thomas Streicher @ 2006-05-16 20:20 UTC (permalink / raw)
To: categories
I know that regular monos needn't be closed under composition. One example
being the category of monoids. Are there other *natural* examples, e.g. of
topological kind?
Thomas Streicher
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: regular monos not closed under composition
@ 2006-05-17 9:47 Prof. Peter Johnstone
0 siblings, 0 replies; 2+ messages in thread
From: Prof. Peter Johnstone @ 2006-05-17 9:47 UTC (permalink / raw)
To: categories
On Tue, 16 May 2006, Thomas Streicher wrote:
> I know that regular monos needn't be closed under composition. One example
> being the category of monoids. Are there other *natural* examples, e.g. of
> topological kind?
>
> Thomas Streicher
>
Depends what you mean by topological. In the category of locales, regular
epis aren't closed under composition (equivalently, regular monos aren't
closed under composition in frames): this was proved by Till Plewe, and
is in his paper `Quotient maps of locales' in Appl. Cat. Struct. 8 (2000),
17--44. Another `natural' example (which I regularly use when teaching
category theory to graduate students) is regular epis in Cat.
Peter Johnstone
^ permalink raw reply [flat|nested] 2+ messages in thread
end of thread, other threads:[~2006-05-17 9:47 UTC | newest]
Thread overview: 2+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2006-05-16 20:20 regular monos not closed under composition Thomas Streicher
2006-05-17 9:47 Prof. Peter Johnstone
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).