  We define a 2-category structure (Pre-Orb) on the category of reduced complex
orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category
(Grp) of proper \'etale effective groupoid objects over the complex manifolds.
Both on (Pre-Orb) and (Grp) there are natural equivalence relations on objects:
(a natural extension of) equivalence of orbifold atlases in (Pre-Orb) and
Morita equivalences in (Grp). We prove that F induces a bijection between the
equivalence classes of its source and target.
