Vol. 3, No. 1, 2018

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Hochschild homology, lax codescent, and duplicial structure

Richard Garner, Stephen Lack and Paul Slevin

Vol. 3 (2018), No. 1, 1–31
Abstract

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.

Keywords
comonads, distributive laws, cyclic category, duplicial objects, Hochschild homology
Mathematical Subject Classification 2010
Primary: 18C15, 18D05, 18G30, 19D55
Secondary: 16T05
Milestones
Received: 16 November 2015
Revised: 28 February 2017
Accepted: 14 March 2017
Published: 7 September 2017
Authors
Richard Garner
Department of Mathematics
Macquarie University
North Ryde, NSW
Australia
Stephen Lack
Department of Mathematics
Macquarie University
North Ryde, NSW
Australia
Paul Slevin
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom