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DUALITY FOR CLANS: AN EXTENSION OF GABRIEL–ULMER DUALITY

Part of: Categories and theories Algebraic logic Other classes of algebra

Published online by Cambridge University Press:  15 May 2025

JONAS FREY Open the ORCID record for JONAS FREY [Opens in a new window]
JONAS FREY*
Affiliation:
UNIVERSITÉ SORBONNE PARIS NORD CNRS, LABORATOIRE D’INFORMATIQUE DE PARIS NORD, LIPN F-93430 VILLETANEUSE FRANCE
*
E-mail: frey@lipn.univ-paris13.fr
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Abstract

Clans are categorical representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the locally finitely presentable categories of models via Gabriel–Ulmer duality. Extending Gabriel–Ulmer duality to account for this additional information, we present a duality theory between clans and locally finitely presentable categories equipped with a weak factorization system of a certain kind.

Keywords

functorial semanticsgeneralized algebraic theoryclanGabriel–Ulmer duality

MSC classification

Primary: 18C10: Theories (e.g. algebraic theories), structure, and semantics
Secondary: 08C05: Categories of algebras 03G30: Categorical logic, topoi

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Article
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The Journal of Symbolic Logic , First View , pp. 1 - 38
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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