Polymorphic Automorphisms and the Picard Group

@inproceedings{Hofstra2021PolymorphicAA,
  title={Polymorphic Automorphisms and the Picard Group},
  author={Pieter J. W. Hofstra and Jason Parker and Philip J. Scott},
  booktitle={FSCD},
  year={2021}
}
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… Expand
1 Citations
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