Hochschild homology, lax codescent, and duplicial structure

Richard Garner; Stephen Lack; Paul Slevin

doi:10.2140/akt.2018.3.1

Hochschild homology, lax codescent, and duplicial structure

Richard Garner^*, Stephen Lack, Paul Slevin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 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 language	English
Pages (from-to)	1-31
Number of pages	31
Journal	Annals of k-Theory
Volume	3
Issue number	1
DOIs	https://doi.org/10.2140/akt.2018.3.1
Publication status	Published - 2018

Keywords

comonads
distributive laws
cyclic category
duplicial objects
Hochschild homology

Access to Document

10.2140/akt.2018.3.1

Cite this

@article{2182b3f112724fffa7e38a6a6d843465,

title = "Hochschild homology, lax codescent, and duplicial structure",

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 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.",

keywords = "comonads, distributive laws, cyclic category, duplicial objects, Hochschild homology",

author = "Richard Garner and Stephen Lack and Paul Slevin",

year = "2018",

doi = "10.2140/akt.2018.3.1",

language = "English",

volume = "3",

pages = "1--31",

journal = "Annals of k-Theory",

issn = "2379-1683",

publisher = "MATHEMATICAL SCIENCE PUBL",

number = "1",

}

TY - JOUR

T1 - Hochschild homology, lax codescent, and duplicial structure

AU - Garner, Richard

AU - Lack, Stephen

AU - Slevin, Paul

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - comonads

KW - distributive laws

KW - cyclic category

KW - duplicial objects

KW - Hochschild homology

U2 - 10.2140/akt.2018.3.1

DO - 10.2140/akt.2018.3.1

M3 - Article

SN - 2379-1683

VL - 3

SP - 1

EP - 31

JO - Annals of k-Theory

JF - Annals of k-Theory

IS - 1

ER -

Hochschild homology, lax codescent, and duplicial structure

Abstract

Keywords

Access to Document

Fingerprint

Cite this