Compactly generated stacks: a Cartesian closed theory of topological stacks (Q411643)

Stacks generalise spaces as, in addition, to the space of points they can have non-trivial local automorphisms. A stack is a `lax presheaf' of groupoids satisfying a descent condition. Topological stacks are stacks on the category \(Top\) of compactly generated spaces with the étale (Grothendieck) topology, which are representable by a topological groupoid.NEWLINENEWLINEThe category \(Top\) is well known to be Cartesian closed, but the (bi)category of topological stacks appears neither to be complete nor Cartesian closed. In this paper, the author proposes a new Grothendieck topology for which the (bi)category of topological stacks \textit{is} Cartesian closed. Several interesting and useful consequences of this are explored in depth.