Hofstra, P;
Karvonen, M;
(2024)
Inner autoequivalences in general and those of monoidal categories in particular.
Journal of Pure and Applied Algebra
, 228
(11)
, Article 107717. 10.1016/j.jpaa.2024.107717.
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Abstract
We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence of binary coproducts, unifying various known one-dimensional results and providing tractable computational tools in the two-dimensional setting. In particular, we show that the isotropy 2-group of a monoidal category coincides with its Picard 2-group, i.e., the 2-group on its weakly invertible objects.
| Type: | Article |
|---|---|
| Title: | Inner autoequivalences in general and those of monoidal categories in particular |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jpaa.2024.107717 |
| Publisher version: | http://dx.doi.org/10.1016/j.jpaa.2024.107717 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Picard 2-group, 2-category, 2-group, Inner autoequivalence, Dense pseudofunctor |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10193404 |
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