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URN: urn:nbn:de:0030-drops-153656
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On Doctrines and Cartesian Bicategories

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Abstract

We study the relationship between cartesian bicategories and a specialisation of Lawvere’s hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in algebraic terms based on a string diagrammatic calculus, the latter in universal terms using the fundamental notion of adjoint functor. We prove that these two approaches are related by an adjunction, which can be strengthened to an equivalence by imposing further constraints on doctrines.

BibTeX - Entry

@InProceedings{bonchi_et_al:LIPIcs.CALCO.2021.10,
  author =	{Bonchi, Filippo and Santamaria, Alessio and Seeber, Jens and Soboci\'{n}ski, Pawe{\l}},
  title =	{{On Doctrines and Cartesian Bicategories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15365},
  URN =		{urn:nbn:de:0030-drops-153656},
  doi =		{10.4230/LIPIcs.CALCO.2021.10},
  annote =	{Keywords: Cartesian bicategories, elementary existential doctrines, string diagram}
}

Keywords: Cartesian bicategories, elementary existential doctrines, string diagram
Seminar: 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
Issue date: 2021
Date of publication: 08.11.2021


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