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2018 Hochschild homology, lax codescent, and duplicial structure
Richard Garner, Stephen Lack, Paul Slevin
Ann. K-Theory 3(1): 1-31 (2018). DOI: 10.2140/akt.2018.3.1

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.

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Richard Garner. Stephen Lack. Paul Slevin. "Hochschild homology, lax codescent, and duplicial structure." Ann. K-Theory 3 (1) 1 - 31, 2018. https://doi.org/10.2140/akt.2018.3.1

Information

Received: 16 November 2015; Revised: 28 February 2017; Accepted: 14 March 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06775609
MathSciNet: MR3695362
Digital Object Identifier: 10.2140/akt.2018.3.1

Subjects:
Primary: 18C15 , 18D05 , 18G30 , 19D55
Secondary: 16T05

Keywords: comonads , cyclic category , distributive laws , duplicial objects , Hochschild homology

Rights: Copyright © 2018 Mathematical Sciences Publishers

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