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On dualizability and invertibility in the higher Morita category
Abstract
We prove a conjecture of Lurie characterizing (n+1)-dualizability in higher Morita categories of 𝔼n-algebras in terms of dualizability over certain factorization homologies. A key ingredient is a higher Morita category based on the recently developed framework of pointless factorization algebras of Karlsson and the first author. We also verify an invertibility conjecture of Brochier--Jordan--Safranov--Snyder as an immediate corollary of our main result. Moreover, we prove a relative version of the dualizability conjecture, yielding a new criterion for relative/twisted field theories. We give some examples, including Dirichlet and Neumann relative theories.
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BibTeX
@misc{scheimbauer2026dualizability,
title = {{On dualizability and invertibility in the higher Morita category}},
author = {Claudia Scheimbauer and Pelle Steffens and William Stewart},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16953},
eprint = {2607.16953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16953},
}
RIS
TY - UNPB
TI - On dualizability and invertibility in the higher Morita category
AU - Claudia Scheimbauer
AU - Pelle Steffens
AU - William Stewart
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2607.16953
UR - https://arxiv.org/abs/2607.16953
AB - We prove a conjecture of Lurie characterizing (n+1)-dualizability in higher Morita categories of 𝔼_n-algebras in terms of dualizability over certain factorization homologies. A key ingredient is a higher Morita category based on the recently developed framework of pointless factorization algebras of Karlsson and the first author. We also verify an invertibility conjecture of Brochier--Jordan--Safranov--Snyder as an immediate corollary of our main result. Moreover, we prove a relative version of the dualizability conjecture, yielding a new criterion for relative/twisted field theories. We give some examples, including Dirichlet and Neumann relative theories.
ER -