Article

On Well-Founded and Recursive Coalgebras

Authors:

Jiří Adámek,

Lawrence S. MossAuthors Info & Claims

Foundations of Software Science and Computation Structures: 23rd International Conference, FOSSACS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, Proceedings

Pages 17 - 36

https://doi.org/10.1007/978-3-030-45231-5_2

Published: 25 April 2020 Publication History

Abstract

This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor’s General Recursion Theorem that every well-founded coalgebra is recursive, and we study conditions which imply the converse. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.

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Cited By

Wißmann TMilius SSobocinski PLago UEsparza J(2024)Initial Algebras Unchained - A Novel Initial Algebra Construction Formalized in AgdaProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662105(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662105
Heerdt GKappé TRot JSammartino MSilva A(2022)A Categorical Framework for Learning Generalised Tree AutomataCoalgebraic Methods in Computer Science10.1007/978-3-031-10736-8_4(67-87)Online publication date: 2-Apr-2022
https://dl.acm.org/doi/10.1007/978-3-031-10736-8_4

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cover image Guide Proceedings

Foundations of Software Science and Computation Structures: 23rd International Conference, FOSSACS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, Proceedings

Apr 2020

656 pages

ISBN:978-3-030-45230-8

DOI:10.1007/978-3-030-45231-5

Editors:
Jean Goubault-Larrecq
ENS/CNRS, Université Paris-Saclay, Cachan, France
,
Barbara König
University of Duisburg-Essen, Duisburg, Germany

© The Author(s) 2020.

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 25 April 2020

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Cited By

Wißmann TMilius SSobocinski PLago UEsparza J(2024)Initial Algebras Unchained - A Novel Initial Algebra Construction Formalized in AgdaProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662105(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662105
Heerdt GKappé TRot JSammartino MSilva A(2022)A Categorical Framework for Learning Generalised Tree AutomataCoalgebraic Methods in Computer Science10.1007/978-3-031-10736-8_4(67-87)Online publication date: 2-Apr-2022
https://dl.acm.org/doi/10.1007/978-3-031-10736-8_4

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