Fantechi — Stacks For Everybody (2001)

Let S be a category with a Grothendieck topology. A stack over S is a category fibered in groupoids over S, such that isomorphisms form a sheaf and every descent datum is effective. If S is the category of schemes with the \textasciiacute etale topology, a stack is algebraic in the sense of Deligne-Mumford (respectively Artin) if it has an \textasciiacute etale (resp. smooth) presentation.