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Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von 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.