Stable homotopy hypothesis in the Tamsamani model

Lyne Moser; Viktoriya Ozornova; Simona Paoli; Maru Sarazola; Paula Verdugo

doi:10.1016/j.topol.2022.108106

Stable homotopy hypothesis in the Tamsamani model

Lyne Moser, Viktoriya Ozornova^*, Simona Paoli, Maru Sarazola, Paula Verdugo

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We prove that symmetric monoidal weak n-groupoids in the Tamsamani model provide a model for stable n-types. Moreover, we recover the classical statement that Picard categories model stable 1-types.

Original language	English
Article number	108106
Number of pages	40
Journal	Topology and its Applications
Volume	316
Early online date	13 Jun 2022
DOIs	https://doi.org/10.1016/j.topol.2022.108106
Publication status	Published - 1 Jul 2022

Bibliographical note

Funding Information:
This project arose as a part of the Women in Topology III program. We would like to thank the organizers for making this collaboration possible. We would also like to thank the Hausdorff Research Institute for Mathematics, NSF-DMS 1901795, NSF-HRD 1500481 - AWM ADVANCE grant and Foundation Compositio Mathematica (grant number 386) for supporting this program. Our special thanks go to Angélica Osorno, to whom we owe the original impetus of this project, and who supported us throughout the work on it. The fifth-named author acknowledges the financial support of an international Macquarie University Research Excellence Scholarship.

Keywords

Spectra
Stable homotopy hypothesis
Symmetric monoidal categories
Tamsamani n-categories

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title = "Stable homotopy hypothesis in the Tamsamani model",

abstract = "We prove that symmetric monoidal weak n-groupoids in the Tamsamani model provide a model for stable n-types. Moreover, we recover the classical statement that Picard categories model stable 1-types.",

keywords = "Spectra, Stable homotopy hypothesis, Symmetric monoidal categories, Tamsamani n-categories",

author = "Lyne Moser and Viktoriya Ozornova and Simona Paoli and Maru Sarazola and Paula Verdugo",

note = "Funding Information: This project arose as a part of the Women in Topology III program. We would like to thank the organizers for making this collaboration possible. We would also like to thank the Hausdorff Research Institute for Mathematics, NSF-DMS 1901795, NSF-HRD 1500481 - AWM ADVANCE grant and Foundation Compositio Mathematica (grant number 386) for supporting this program. Our special thanks go to Ang{\'e}lica Osorno, to whom we owe the original impetus of this project, and who supported us throughout the work on it. The fifth-named author acknowledges the financial support of an international Macquarie University Research Excellence Scholarship. ",

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AU - Ozornova, Viktoriya

AU - Paoli, Simona

AU - Sarazola, Maru

AU - Verdugo, Paula

N1 - Funding Information: This project arose as a part of the Women in Topology III program. We would like to thank the organizers for making this collaboration possible. We would also like to thank the Hausdorff Research Institute for Mathematics, NSF-DMS 1901795, NSF-HRD 1500481 - AWM ADVANCE grant and Foundation Compositio Mathematica (grant number 386) for supporting this program. Our special thanks go to Angélica Osorno, to whom we owe the original impetus of this project, and who supported us throughout the work on it. The fifth-named author acknowledges the financial support of an international Macquarie University Research Excellence Scholarship.

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AB - We prove that symmetric monoidal weak n-groupoids in the Tamsamani model provide a model for stable n-types. Moreover, we recover the classical statement that Picard categories model stable 1-types.

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KW - Stable homotopy hypothesis

KW - Symmetric monoidal categories

KW - Tamsamani n-categories

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ER -

Stable homotopy hypothesis in the Tamsamani model

Abstract

Bibliographical note

Keywords

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