17 May
2006
17 May
'06
7:47 p.m.
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