MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Are there non-regular strong monics in the category of locales?

share|cite|improve this question
up vote 5 down vote accepted

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—hence every strong monic of locales is regular.

share|cite|improve this answer
Yep. Just found it myself in Sketches of an Elephant A.1.3.4. Thank you, though! – John Iskra Jan 4 '10 at 23:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.