∞-operads as symmetric monoidal ∞-categories

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Standard

∞-operads as symmetric monoidal ∞-categories. / Haugseng, Rune Gjøringbø; Kock, Joachim.

I: Publicacions Matematiques, Bind 68, Nr. 1, 2024, s. 111-137.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Haugseng, RG & Kock, J 2024, '∞-operads as symmetric monoidal ∞-categories', Publicacions Matematiques, bind 68, nr. 1, s. 111-137. https://doi.org/10.5565/PUBLMAT6812406

APA

Haugseng, R. G., & Kock, J. (2024). ∞-operads as symmetric monoidal ∞-categories. Publicacions Matematiques, 68(1), 111-137. https://doi.org/10.5565/PUBLMAT6812406

Vancouver

Haugseng RG, Kock J. ∞-operads as symmetric monoidal ∞-categories. Publicacions Matematiques. 2024;68(1):111-137. https://doi.org/10.5565/PUBLMAT6812406

Author

Haugseng, Rune Gjøringbø ; Kock, Joachim. / ∞-operads as symmetric monoidal ∞-categories. I: Publicacions Matematiques. 2024 ; Bind 68, Nr. 1. s. 111-137.

Bibtex

@article{4f43c27c9aaa4c7c9c2835b91e856277,
title = "∞-operads as symmetric monoidal ∞-categories",
abstract = "We use Lurie{\textquoteright}s symmetric monoidal envelope functor to give two new descriptions of∞-operads: as certain symmetric monoidal ∞-categories whose underlying symmetric monoidal∞-groupoids are free, and as certain symmetric monoidal ∞-categories equipped with a symmetricmonoidal functor to finite sets (with disjoint union as tensor product). The latter leads to a thirddescription of ∞-operads, as a localization of a presheaf ∞-category, and we use this to give a simpleproof of the equivalence between Lurie{\textquoteright}s and Barwick{\textquoteright}s models for ∞-operads.2020 Mathemati",
author = "Haugseng, {Rune Gj{\o}ringb{\o}} and Joachim Kock",
year = "2024",
doi = "10.5565/PUBLMAT6812406",
language = "English",
volume = "68",
pages = "111--137",
journal = "Publicacions Matematiques",
issn = "0214-1493",
publisher = "Universitat Autonoma de Barcelona * Servei de Publicacions",
number = "1",

}

RIS

TY - JOUR

T1 - ∞-operads as symmetric monoidal ∞-categories

AU - Haugseng, Rune Gjøringbø

AU - Kock, Joachim

PY - 2024

Y1 - 2024

N2 - We use Lurie’s symmetric monoidal envelope functor to give two new descriptions of∞-operads: as certain symmetric monoidal ∞-categories whose underlying symmetric monoidal∞-groupoids are free, and as certain symmetric monoidal ∞-categories equipped with a symmetricmonoidal functor to finite sets (with disjoint union as tensor product). The latter leads to a thirddescription of ∞-operads, as a localization of a presheaf ∞-category, and we use this to give a simpleproof of the equivalence between Lurie’s and Barwick’s models for ∞-operads.2020 Mathemati

AB - We use Lurie’s symmetric monoidal envelope functor to give two new descriptions of∞-operads: as certain symmetric monoidal ∞-categories whose underlying symmetric monoidal∞-groupoids are free, and as certain symmetric monoidal ∞-categories equipped with a symmetricmonoidal functor to finite sets (with disjoint union as tensor product). The latter leads to a thirddescription of ∞-operads, as a localization of a presheaf ∞-category, and we use this to give a simpleproof of the equivalence between Lurie’s and Barwick’s models for ∞-operads.2020 Mathemati

U2 - 10.5565/PUBLMAT6812406

DO - 10.5565/PUBLMAT6812406

M3 - Journal article

VL - 68

SP - 111

EP - 137

JO - Publicacions Matematiques

JF - Publicacions Matematiques

SN - 0214-1493

IS - 1

ER -

ID: 382851002