Hochschild homology, lax codescent, and duplicial structure

Richard Garner*, Stephen Lack, Paul Slevin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalAnnals of k-Theory
Issue number1
Publication statusPublished - 2018


  • comonads
  • distributive laws
  • cyclic category
  • duplicial objects
  • Hochschild homology

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