Operadic categories and decalage

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Operadic categories and decalage. / Garner, Richard; Kock, Joachim; Weber, Mark.

In: Advances in Mathematics, Vol. 377, 107440, 22.01.2021.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Garner, R, Kock, J & Weber, M 2021, 'Operadic categories and decalage', Advances in Mathematics, vol. 377, 107440. https://doi.org/10.1016/j.aim.2020.107440

APA

Garner, R., Kock, J., & Weber, M. (2021). Operadic categories and decalage. Advances in Mathematics, 377, [107440]. https://doi.org/10.1016/j.aim.2020.107440

Vancouver

Garner R, Kock J, Weber M. Operadic categories and decalage. Advances in Mathematics. 2021 Jan 22;377. 107440. https://doi.org/10.1016/j.aim.2020.107440

Author

Garner, Richard ; Kock, Joachim ; Weber, Mark. / Operadic categories and decalage. In: Advances in Mathematics. 2021 ; Vol. 377.

Bibtex

@article{9e747be33810424c8122adeaa45ba19a,
title = "Operadic categories and decalage",
abstract = "Batanin and Markl's operadic categories are categories in which each map is endowed with a finite collection of {"}abstract fibres{"}-also objects of the same category-subject to suitable axioms. We give a reconstruction of the data and axioms of operadic categories in terms of the decalage comonad Don small categories. A simple case involves unaryoperadic categories-ones wherein each map has exactly one abstract fibre-which are exhibited as categories which are, first of all, coalgebras for the comonad D, and, furthermore, algebras for the monad (D) over tilde induced on Cat(D) by the forgetful-cofree adjunction. A similar description is found for general operadic categories arising out of a corresponding analysis that starts from a {"}modified decalage{"} comonad D-m on the arrow category Cat(2). (C) 2020 Elsevier Inc. All rights reserved.",
keywords = "Operadic categories, 2-Segal spaces, Decalage",
author = "Richard Garner and Joachim Kock and Mark Weber",
year = "2021",
month = jan,
day = "22",
doi = "10.1016/j.aim.2020.107440",
language = "English",
volume = "377",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Operadic categories and decalage

AU - Garner, Richard

AU - Kock, Joachim

AU - Weber, Mark

PY - 2021/1/22

Y1 - 2021/1/22

N2 - Batanin and Markl's operadic categories are categories in which each map is endowed with a finite collection of "abstract fibres"-also objects of the same category-subject to suitable axioms. We give a reconstruction of the data and axioms of operadic categories in terms of the decalage comonad Don small categories. A simple case involves unaryoperadic categories-ones wherein each map has exactly one abstract fibre-which are exhibited as categories which are, first of all, coalgebras for the comonad D, and, furthermore, algebras for the monad (D) over tilde induced on Cat(D) by the forgetful-cofree adjunction. A similar description is found for general operadic categories arising out of a corresponding analysis that starts from a "modified decalage" comonad D-m on the arrow category Cat(2). (C) 2020 Elsevier Inc. All rights reserved.

AB - Batanin and Markl's operadic categories are categories in which each map is endowed with a finite collection of "abstract fibres"-also objects of the same category-subject to suitable axioms. We give a reconstruction of the data and axioms of operadic categories in terms of the decalage comonad Don small categories. A simple case involves unaryoperadic categories-ones wherein each map has exactly one abstract fibre-which are exhibited as categories which are, first of all, coalgebras for the comonad D, and, furthermore, algebras for the monad (D) over tilde induced on Cat(D) by the forgetful-cofree adjunction. A similar description is found for general operadic categories arising out of a corresponding analysis that starts from a "modified decalage" comonad D-m on the arrow category Cat(2). (C) 2020 Elsevier Inc. All rights reserved.

KW - Operadic categories

KW - 2-Segal spaces

KW - Decalage

U2 - 10.1016/j.aim.2020.107440

DO - 10.1016/j.aim.2020.107440

M3 - Journal article

VL - 377

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 107440

ER -

ID: 331497046