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FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE

Published online by Cambridge University Press:  19 February 2021

THEO JOHNSON-FREYD Open the ORCID record for THEO JOHNSON-FREYD [Opens in a new window]  and
MATTHEW YU Open the ORCID record for MATTHEW YU [Opens in a new window]
THEO JOHNSON-FREYD
Affiliation:
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada and Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada e-mail: theojf@dal.ca, theojf@pitp.ca
MATTHEW YU*
Affiliation:
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
*
e-mail: myu@perimeterinstitute.ca
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Abstract

We show that if ${\mathcal C}$ is a fusion $2$ -category in which the endomorphism category of the unit object is or , then the indecomposable objects of ${\mathcal C}$ form a finite group.

Keywords

categorical Schur’s lemmafusion 2-categorystate-operator correspondence
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 434 - 442
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The Perimeter Institute is in the Haldimand Tract, land promised to the Six Nations. Dalhousie University is in Mi‘kma‘ki, the ancestral and unceded territory of the Mi‘kmaq. We are all Treaty people.

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