Perhaps a bicategory B which is "locally a topos" (i.e. whose hom-categories B(u,v) are topoi and for which B(f,g) is a geom morphism for all arrows f, g) might be called a *biallegory*. These provide a setting for "stacks". Of course, Peter's categories A are then those with SpanA a biallegory. Ross ++++++++++++++++++++++++++++++++++