  We define and study the notions of ribbon dioperads and modular ribbon
properads. We give a Lie algebra structure on the colimit total object and the
limit total object of a ribbon dioperad, and we give a norm map between them.
We give a cobar construction for dg ribbon co-dioperads. We also prove similar
results for modular ribbon properads. These results are applied to the study of
higher Hochschild cochain complexes and pre-Calabi-Yau categories.
