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Orbifolds as a localization of the 2-category of groupoids

Eugene Lerman
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Abstract

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category structure drops down to the localization. In our construction the spaces of 1- and 2-arrows admit natural topologies, the space of morphisms (1-arrows) between two orbifolds is naturally a groupoid and the symmetries of an orbifold form a strict 2-group.

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Eugene Lerman. 2010-08-31. Orbifolds as a localization of the 2-category of groupoids. https://arxiv.org/abs/math/0608396

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