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Hochschild homology, lax
codescent, and duplicial structure
Richard Garner, Stephen Lack and Paul Slevin |
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Vol. 3 (2018), No. 1, 1–31
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DOI: 10.2140/akt.2018.3.1
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Abstract |
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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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Keywords
comonads, distributive laws, cyclic category, duplicial
objects, Hochschild homology
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Mathematical Subject Classification 2010
Primary: 18C15, 18D05, 18G30, 19D55
Secondary: 16T05
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Milestones
Received: 16 November 2015
Revised: 28 February 2017
Accepted: 14 March 2017
Published: 7 September 2017
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Authors |
| Richard Garner | |
| Department of Mathematics Macquarie University North Ryde, NSW Australia |
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| Stephen Lack | |
| Department of Mathematics Macquarie University North Ryde, NSW Australia |
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| Paul Slevin | |
| School of Mathematics and
Statistics University of Glasgow Glasgow United Kingdom |
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