On dualizability and invertibility in the higher Morita category

Claudia Scheimbauer; Pelle Steffens; William Stewart

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arXiv · 2607.16953

On dualizability and invertibility in the higher Morita category

Claudia Scheimbauer·Pelle Steffens·William Stewart

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Abstract

We prove a conjecture of Lurie characterizing $(n+1)$-dualizability in higher Morita categories of $\mathbb{E}_n$-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.

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Claudia Scheimbauer, Pelle Steffens, William Stewart. 2026-07-18. On dualizability and invertibility in the higher Morita category. https://arxiv.org/abs/2607.16953

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