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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.
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Hofstra et al. (Fri,) studied this question.
www.synapsesocial.com/papers/68e6999bb6db64358761f406 — DOI: https://doi.org/10.1016/j.jpaa.2024.107717
Pieter Hofstra
Martti Karvonen
Journal of Pure and Applied Algebra
University of Ottawa
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