Oberseminar WiSe 12/13 Abstract to the talk of Matteo Tommasini
Orbifolds as 2-categories
It is known that orbifolds in differentiable/complex geometry are the counterpart of (Deligne-Mumford) stacks in algebraic geometry. The latter form not only a category (stacks and morphisms of them), but also a non-trivial 2-category. An analogous structure exists also on "intermediate" objects between orbifolds and stacks, namely groupoids.
Therefore it seems reasonable that a 2-category structure also exists on the side of orbifolds. I'll present some partial results in this direction (see arXiv:1008.0988) and discuss possible further developments.