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arXiv · 2102.11081

Polymorphic Automorphisms and the Picard Group

Pieter Hofstra·Jason Parker·Philip J. Scott
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Abstract

We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant isotropy group) associated with an algebraic theory to the wider class of quasi-equational theories. We apply this characterization to prove that the isotropy group of a strict monoidal category is precisely its Picard group of invertible objects. Furthermore, we obtain an explicit description of the covariant isotropy group of a presheaf category.

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Pieter Hofstra, Jason Parker, Philip J. Scott. 2021-02-22. Polymorphic Automorphisms and the Picard Group. https://arxiv.org/abs/2102.11081

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