License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2019.15
URN: urn:nbn:de:0030-drops-114439
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11443/
Bonchi, Filippo ;
Seeber, Jens ;
Sobocinski, Pawel
The Axiom of Choice in Cartesian Bicategories
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}
}
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Keywords: |
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Cartesian bicategories, Axiom of choice, string diagrams |
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Collection: |
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8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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25.11.2019 |
