License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2021.26
URN: urn:nbn:de:0030-drops-142646
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14264/
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Hofstra, Pieter ; Parker, Jason ; Scott, Philip J.

Polymorphic Automorphisms and the Picard Group

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LIPIcs-FSCD-2021-26.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{hofstra_et_al:LIPIcs.FSCD.2021.26,
  author =	{Hofstra, Pieter and Parker, Jason and Scott, Philip J.},
  title =	{{Polymorphic Automorphisms and the Picard Group}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14264},
  URN =		{urn:nbn:de:0030-drops-142646},
  doi =		{10.4230/LIPIcs.FSCD.2021.26},
  annote =	{Keywords: Partial Horn Theories, Monoidal Categories, Definable Automorphisms, Polymorphism, Indeterminates, Normal Forms}
}

Keywords: Partial Horn Theories, Monoidal Categories, Definable Automorphisms, Polymorphism, Indeterminates, Normal Forms
Collection: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue Date: 2021
Date of publication: 06.07.2021

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