2
$\begingroup$

Is the inclusion of the category of sheaves into the category of presheaves monadic? If not, then maybe it preserves directed colimits?

$\endgroup$
2
  • $\begingroup$ Ok. I think the answer is no. Sorry for disturbing. $\endgroup$
    – thinker
    Dec 18, 2011 at 16:17
  • $\begingroup$ The answer to the second question is "not in general", but it is true that it will always be accessible, i.e. preserve sufficiently-highly-filtered colimits. For some purposes that is good enough. $\endgroup$ Dec 20, 2011 at 1:17

1 Answer 1

5
$\begingroup$

The answer (to the first question) is yes: reflections are always monadic, and the associated monad is idempotent.

$\endgroup$
1
  • $\begingroup$ Thanks. It is nice to know such general result. I still think that the answer for second question is no. $\endgroup$
    – thinker
    Dec 18, 2011 at 20:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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