A convenient 2-category of topological stacks is constructed which is both
complete and Cartesian closed. This 2-category, called the 2-category of
compactly generated stacks, is the analogue of classical topological stacks,
but for a different Grothendieck topology. In fact, there is an equivalence of
2-categories between compactly generated stacks and those classical topological
stacks which admit locally compact atlases. Compactly generated stacks are also
equivalent to a bicategory of topological groupoids and principal bundles, just
as in the classical case.