  A convenient bicategory of topological stacks is constructed which is both
complete and Cartesian closed. This bicategory, called the bicategory of
compactly generated stacks, is the analogue of classical topological stacks,
but for a different Grothendieck topology. In fact, there is an equivalence of
bicategories between compactly generated stacks and those classical topological
stacks which admit locally compact Hausdorff atlases. Compactly generated
stacks are also equivalent to a bicategory of topological groupoids and
principal bundles, just as in the classical case. If a classical topological
stack and a compactly generated stack have a presentation by the same
topological groupoid, then they restrict to the same stack over locally compact
Hausdorff spaces and are homotopy equivalent.
