Hochschild homology, lax codescent, and duplicial structure

The duplicial objects of Dwyer and Kan are a generalization of the cyclic
objects of Connes. I will describe these duplicial objects in terms of the decalage
comonads, and give a conceptual account of a construction of duplicial objects due
to Böhm and  Stefan. This is done in terms of a 2-categorical generalization of
Hochschild homology. If time permits, I will also discuss duplicial structure on nerves
of categories, bicategories, and monoidal categories.