Compactly Generated Stacks

From CRCG-Wiki

The existence of a space of maps between two topological spaces is natural to desire, which is why most topologists restrict their attention to compactly generated Hausdorff spaces. The existence of a topological stack of maps between two topological stacks is also of importance, in light of moduli-theory. However, topological stacks appear to be lacking in this respect and furthermore seem to only have finite limits. In this talk, I will introduce the theory of compactly generated stacks, which solve both of these problems. Compactly generated stacks are “essentially the same” as topological stacks, and moreover, turn out to be equivalent to a full sub-2-category thereof.