Antipodes of monoidal decomposition spaces

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Antipodes of monoidal decomposition spaces. / Carlier, Louis; Kock, Joachim.

I: Communications in Contemporary Mathematics, Bind 22, Nr. 2, 1850081, 03.2020.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Carlier, L & Kock, J 2020, 'Antipodes of monoidal decomposition spaces', Communications in Contemporary Mathematics, bind 22, nr. 2, 1850081. https://doi.org/10.1142/S0219199718500815

APA

Carlier, L., & Kock, J. (2020). Antipodes of monoidal decomposition spaces. Communications in Contemporary Mathematics, 22(2), [1850081]. https://doi.org/10.1142/S0219199718500815

Vancouver

Carlier L, Kock J. Antipodes of monoidal decomposition spaces. Communications in Contemporary Mathematics. 2020 mar.;22(2). 1850081. https://doi.org/10.1142/S0219199718500815

Author

Carlier, Louis ; Kock, Joachim. / Antipodes of monoidal decomposition spaces. I: Communications in Contemporary Mathematics. 2020 ; Bind 22, Nr. 2.

Bibtex

@article{cb52a073602c4b24a20f8b0af16e1852,
title = "Antipodes of monoidal decomposition spaces",
abstract = "We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Mobius function as mu = zeta o S, just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors S-even - S-odd, and it is a refinement of the general Mobius inversion construction of Galvez-Kock-Tonks, but exploiting the monoidal structure.",
keywords = "Bialgebra, antipode, decomposition space, 2-Segal space, incidence algebra, BIALGEBRAS",
author = "Louis Carlier and Joachim Kock",
year = "2020",
month = mar,
doi = "10.1142/S0219199718500815",
language = "English",
volume = "22",
journal = "Communications in Contemporary Mathematics",
issn = "0219-1997",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

RIS

TY - JOUR

T1 - Antipodes of monoidal decomposition spaces

AU - Carlier, Louis

AU - Kock, Joachim

PY - 2020/3

Y1 - 2020/3

N2 - We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Mobius function as mu = zeta o S, just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors S-even - S-odd, and it is a refinement of the general Mobius inversion construction of Galvez-Kock-Tonks, but exploiting the monoidal structure.

AB - We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Mobius function as mu = zeta o S, just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors S-even - S-odd, and it is a refinement of the general Mobius inversion construction of Galvez-Kock-Tonks, but exploiting the monoidal structure.

KW - Bialgebra

KW - antipode

KW - decomposition space

KW - 2-Segal space

KW - incidence algebra

KW - BIALGEBRAS

U2 - 10.1142/S0219199718500815

DO - 10.1142/S0219199718500815

M3 - Journal article

VL - 22

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 2

M1 - 1850081

ER -

ID: 331497757