Welcome to MathOverflow

Question

1

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

flag	asked Dec 18 2011 at 16:02 thinker 11●1

	Ok. I think the answer is no. Sorry for disturbing. – thinker Dec 18 2011 at 16:17
	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. – Mike Shulman Dec 20 2011 at 1:17

Finn Lawler · Answer 1 · 2011-12-18 19:19:04Z UTC

4

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

answered Dec 18 2011 at 19:19

Finn Lawler
2,361●1●5●11

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

Monadicity and sheaves.