  We study three variants of bicategories of diffeological groupoids, and show
that they are all equivalent: the bicategory with generalised morphisms, the
bicategory with anafunctors, and the bicategory with bibundles. Moreover, we
show that the corresponding sub-bicategories of locally subductive
diffeological groupoids, as well as Lie groupoids, are (essentially) full
sub-bicategories. As applications, we obtain equivalences with the
corresponding 2-categories of geometric stacks, and present some Morita
invariants.

Differential Geometry;Category Theory