# Is every (Artin/DM) algebraic stack fibered in sets an algebraic space?

If $X$ is an algebraic stack fibered in sets (and therefore essentially a sheaf), is it an algebraic space? It seems conceivable that at least when $X$ is Deligne-Mumford, it is actually an algebraic space. However, when $X$ is an Artin stack, it is only required to have an atlas of smooth maps of affines, so it seems less likely that this would be the case.

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A more practical version of the question is to impose the weaker-looking requirement that geometric points have trivial automorphism functors rather than the more "global" hypothesis that the groupoids are sets. This also has an affirmative answer, but it doesn't appear to be stated in the book by L. & M-B. (It is an exercise to show that the hypothesis on geometric pts implies the sheaf/set property for the fibered category, given that one is working with an Artin stack, understood to satisfy the diagonal requirements as in the L-MB book.) –  BCnrd Oct 11 '10 at 21:45