Comonad cohomology of track categories

David Blanc; Simona Paoli

doi:10.1007/s40062-019-00235-2

Comonad cohomology of track categories

David Blanc, Simona Paoli^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

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

Abstract

We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding (S,O)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the (S,O)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.

Original language	English
Pages (from-to)	881-917
Number of pages	37
Journal	Journal of Homotopy and Related Structures
Volume	14
Issue number	4
Early online date	14 May 2019
DOIs	https://doi.org/10.1007/s40062-019-00235-2
Publication status	Published - Dec 2019

Bibliographical note

Funding Information:
We would like to thank the referee for his or her pertinent and helpful comments. The first author was supported by the Israel Science Foundation grants 74/11 and 770/16.

Keywords

Comonad cohomology
Simplicial category
Track category

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10.1007/s40062-019-00235-2Licence: CC BY

Blanc_JHRS_Comonadchomologytrack_VOR
http://creativecommons.org/licenses/by/4.0/
Final published version, 566 KBLicence: CC BY

Cite this

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abstract = "We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding (S,O)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the (S,O)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.",

keywords = "Comonad cohomology, Simplicial category, Track category",

author = "David Blanc and Simona Paoli",

note = "Funding Information: We would like to thank the referee for his or her pertinent and helpful comments. The first author was supported by the Israel Science Foundation grants 74/11 and 770/16. ",

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AU - Paoli, Simona

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PY - 2019/12

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N2 - We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding (S,O)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the (S,O)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.

AB - We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding (S,O)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the (S,O)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.

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KW - Simplicial category

KW - Track category

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DO - 10.1007/s40062-019-00235-2

M3 - Article

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JF - Journal of Homotopy and Related Structures

IS - 4

ER -

Comonad cohomology of track categories

Abstract

Bibliographical note

Keywords

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