Abstract
We introduce rigid algebras, a generalization of rigid categories to arbitrary symmetric monoidal (Formula presented) -categories. We develop their general theory, showing in particular that the a priori (Formula presented) -category of rigid algebras is in fact an (Formula presented) -category. For the (Formula presented) -category of cospans in an (Formula presented) -category (Formula presented), we show that the (Formula presented) -category of rigid commutative algebras is canonically identified with (Formula presented). This identification is used to construct an adjunction between the cospan construction and the functor assigning to a symmetric monoidal (Formula presented) -category its (Formula presented) -category of rigid commutative algebras.
| Original language | English |
|---|---|
| Journal | International Mathematics Research Notices |
| Volume | 2026 |
| Issue number | 10 |
| DOIs | |
| State | Published - May 2026 |
Bibliographical note
Publisher Copyright:© The Author(s) 2026. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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