Hochschild homology, lax codescent, and duplicial structure

Richard Garner, Stephen Lack, Paul Slevin
2018 Annals of K-theory  
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 Bohm and Stefan. 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.
doi:10.2140/akt.2018.3.1 fatcat:5k5gvraupvf45jb7wpdswh3m7y