most recent 30 from http://mathoverflow.net 2013-05-22T22:20:33Z http://mathoverflow.net/feeds/question/10718 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/10718/strong-monics-in-the-category-of-locales John Iskra 2010-01-04T16:47:49Z 2011-02-03T06:26:12Z

<p>Are there non-regular strong monics in the category of locales?</p>

http://mathoverflow.net/questions/10718/strong-monics-in-the-category-of-locales/10745#10745 Mike Shulman 2010-01-04T22:47:13Z 2010-01-04T22:47:13Z

<p>No. The category of locales is dual to the category of frames, which is monadic (in fact, equationally presented) over Set. Any such category is Barr-exact, and in particular a regular category, which implies that every strong epic of frames is regular&mdash;hence every strong monic of locales is regular.</p>