∞-operads as symmetric monoidal ∞-categories
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∞-operads as symmetric monoidal ∞-categories. / Haugseng, Rune Gjøringbø; Kock, Joachim.
In: Publicacions Matematiques, Vol. 68, No. 1, 2024, p. 111-137.Research output: Contribution to journal › Journal article › Research › peer-review
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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