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.CALCO.2021.10
URN: urn:nbn:de:0030-drops-153656
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15365/
Bonchi, Filippo ;
Santamaria, Alessio ;
Seeber, Jens ;
Sobociński, Paweł
On Doctrines and Cartesian Bicategories
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 |
|
Collection: |
|
9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021) |
|
Issue Date: |
|
2021 |
|
Date of publication: |
|
08.11.2021 |
