Hochschild homology, lax codescent, and duplicial structure

Richard Garner*, Stephen Lack, Paul Slevin

*Corresponding author for this work

Research output: Contribution to journalArticle


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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