Monoidal Extended Stone Duality

Birkmann F, Urbat H, Milius S (2024)

Publication Type: Conference contribution

Publication year: 2024

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Science and Business Media Deutschland GmbH

Book Volume: 14574 LNCS

Pages Range: 144-165

Conference Proceedings Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Event location: Luxembourg City LU

ISBN: 9783031572272

DOI: 10.1007/978-3-031-57228-9_8

Abstract

Extensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental for proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions, subsuming various incarnations of classical extended Stone and Priestley duality as a special case. Guided by these categorical foundations, we investigate residuation algebras, which are algebraic models of language derivatives, and show the subcategory of derivation algebras to be dually equivalent to the category of profinite ordered monoids, restricting to a duality between boolean residuation algebras and profinite monoids. We further extend this duality to capture relational morphisms of profinite ordered monoids, which dualize to natural morphisms of residuation algebras.

Authors with CRIS profile

Fabian Birkmann Lehrstuhl für Informatik 8 (Theoretische Informatik) Henning Urbat Lehrstuhl für Informatik 8 (Theoretische Informatik) Stefan Milius Lehrstuhl für Informatik 8 (Theoretische Informatik)

How to cite

APA:

Birkmann, F., Urbat, H., & Milius, S. (2024). Monoidal Extended Stone Duality. In Naoki Kobayashi, James Worrell (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 144-165). Luxembourg City, LU: Springer Science and Business Media Deutschland GmbH.

MLA:

Birkmann, Fabian, Henning Urbat, and Stefan Milius. "Monoidal Extended Stone Duality." Proceedings of the 27th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2024 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Luxembourg City Ed. Naoki Kobayashi, James Worrell, Springer Science and Business Media Deutschland GmbH, 2024. 144-165.

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