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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2019.15
URN: urn:nbn:de:0030-drops-114439
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11443/
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Bonchi, Filippo ; Seeber, Jens ; Sobocinski, Pawel

The Axiom of Choice in Cartesian Bicategories

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LIPIcs-CALCO-2019-15.pdf (0.5 MB)


Abstract

We argue that cartesian bicategories, often used as a general categorical algebra of relations, are also a natural setting for the study of the axiom of choice (AC). In this setting, AC manifests itself as an inequation asserting that every total relation contains a map. The generality of cartesian bicategories allows us to separate this formulation from other set-theoretically equivalent properties, for instance that epimorphisms split. Moreover, via a classification result, we show that cartesian bicategories satisfying choice tend to be those that arise from bicategories of spans.

BibTeX - Entry

@InProceedings{bonchi_et_al:LIPIcs:2019:11443,
  author =	{Filippo Bonchi and Jens Seeber and Pawel Sobocinski},
  title =	{{The Axiom of Choice in Cartesian Bicategories}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11443},
  URN =		{urn:nbn:de:0030-drops-114439},
  doi =		{10.4230/LIPIcs.CALCO.2019.15},
  annote =	{Keywords: Cartesian bicategories, Axiom of choice, string diagrams}
}

Keywords: Cartesian bicategories, Axiom of choice, string diagrams
Seminar: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue Date: 2019
Date of publication: 22.11.2019


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