We study the duplicial objects of Dwyer and Kan, which generalize the cyclic objects of Connes. We describe duplicial objects in terms of the decalage comonads, and we give a conceptual account of the construction of duplicial objects due to Böhm and Ştefan. This is done in terms of a 2-categorical generalization of Hochschild homology. We also study duplicial structure on nerves of categories, bicategories, and monoidal categories.
"Hochschild homology, lax codescent, and duplicial structure." Ann. K-Theory 3 (1) 1 - 31, 2018. https://doi.org/10.2140/akt.2018.3.1