Bicategories of diffeological groupoids

Diffeological groupoids have become important in recent years in the study of group actions, foliations, and Lie algebroids. A new paper of van der Schaaf shows that, similar to the Lie groupoid case, there is a bicategory of diffeological groupoids with principal bibundles as one-arrows and biequivariant diffeomorphisms as two-arrows. However, there remained an open question: does a diffeological Morita equivalence between Lie groupoids imply a Lie Morita equivalence? <br>In this talk, we answer this in the affirmative, and one can obtain this answer by jumping between three bicategories of diffeological groupoids: Pronk's bicategory of fractions, Roberts' anafunctor bicategory, and that above; moreover, this procedure seems to be a form of "optimization". <br><br>