I have [again][1] two basic questions about stacks.
 
1) When we consider categories fibered in groupoids, do we always mean *small* groupoids?
 
2) In the proof of Artin's criterion for algebraic spaces/stacks $X/S$ for every point $p \in X$ of finite type over $S$ a "local approximation" $X_p$ is constructed. Then $X = \coprod_p X_p$ does the job. But in order to show that this is actually a scheme in the given universe, we need that the points of finite type constitute a *set*. Perhaps I'm overlooking something trivial here, but I cannot see how we can use Artin's criterions to deduce this.
 
 


  [1]: http://mathoverflow.net/questions/58428/basic-questions-about-stacks