Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals

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

Standard

Decomposition spaces, incidence algebras and Mobius inversion III : The decomposition space of Mobius intervals. / Galvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew.

In: Advances in Mathematics, Vol. 334, 20.08.2018, p. 544-584.

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

Harvard

Galvez-Carrillo, I, Kock, J & Tonks, A 2018, 'Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals', Advances in Mathematics, vol. 334, pp. 544-584. https://doi.org/10.1016/j.aim.2018.03.018

APA

Galvez-Carrillo, I., Kock, J., & Tonks, A. (2018). Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals. Advances in Mathematics, 334, 544-584. https://doi.org/10.1016/j.aim.2018.03.018

Vancouver

Galvez-Carrillo I, Kock J, Tonks A. Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals. Advances in Mathematics. 2018 Aug 20;334:544-584. https://doi.org/10.1016/j.aim.2018.03.018

Author

Galvez-Carrillo, Imma ; Kock, Joachim ; Tonks, Andrew. / Decomposition spaces, incidence algebras and Mobius inversion III : The decomposition space of Mobius intervals. In: Advances in Mathematics. 2018 ; Vol. 334. pp. 544-584.

Bibtex

@article{0108dacfac3547beafed95c062987cf2,
title = "Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals",
abstract = "Decomposition spaces are simplicial infinity-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Mobius decomposition space, a far-reaching generalisation of the notion of Mobius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Mobius intervals, which contains the universal Mobius function (but is not induced by a Mobius category), can be realised as the homotopy cardinality of a Mobius decomposition space U of all Mobius intervals, and that in a certain sense U is universal for Mobius decomposition spaces and CULF functors. (C) 2018 Elsevier Inc. All rights reserved.",
keywords = "decomposition space, 2-Segal space, GULF functor, Mobius interval, Mobius inversion, CATEGORIES",
author = "Imma Galvez-Carrillo and Joachim Kock and Andrew Tonks",
year = "2018",
month = aug,
day = "20",
doi = "10.1016/j.aim.2018.03.018",
language = "English",
volume = "334",
pages = "544--584",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Decomposition spaces, incidence algebras and Mobius inversion III

T2 - The decomposition space of Mobius intervals

AU - Galvez-Carrillo, Imma

AU - Kock, Joachim

AU - Tonks, Andrew

PY - 2018/8/20

Y1 - 2018/8/20

N2 - Decomposition spaces are simplicial infinity-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Mobius decomposition space, a far-reaching generalisation of the notion of Mobius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Mobius intervals, which contains the universal Mobius function (but is not induced by a Mobius category), can be realised as the homotopy cardinality of a Mobius decomposition space U of all Mobius intervals, and that in a certain sense U is universal for Mobius decomposition spaces and CULF functors. (C) 2018 Elsevier Inc. All rights reserved.

AB - Decomposition spaces are simplicial infinity-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Mobius decomposition space, a far-reaching generalisation of the notion of Mobius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Mobius intervals, which contains the universal Mobius function (but is not induced by a Mobius category), can be realised as the homotopy cardinality of a Mobius decomposition space U of all Mobius intervals, and that in a certain sense U is universal for Mobius decomposition spaces and CULF functors. (C) 2018 Elsevier Inc. All rights reserved.

KW - decomposition space

KW - 2-Segal space

KW - GULF functor

KW - Mobius interval

KW - Mobius inversion

KW - CATEGORIES

U2 - 10.1016/j.aim.2018.03.018

DO - 10.1016/j.aim.2018.03.018

M3 - Journal article

VL - 334

SP - 544

EP - 584

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 331498039