  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.
