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From: "Prof. Peter Johnstone"
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Subject: Re: regular monos not closed under composition
Date: Wed, 17 May 2006 10:47:01 +0100 (BST)
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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