Finite coproducts, coregularity and coexactness for profinite interior algebras

2025/09/16 by Matteo De Berardinis, De Berardinis, Matteo
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.13058

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In previous articles, we showed that the category of profinite L-algebras (where L is a normal modal logic with the finite model property) is monadic over Set. Then, we developed sequent calculi for extensions of the language of L with infinitary conjunctions and disjunctions, proving completeness with respect to profinite L-algebras and relating syntactic properties of the calculi with regularity/exactness properties of the category opposite to profinite L-algebras. In this paper, we focus on the algebraic perspective: we characterize those L extending S4 whose profinite algebras enjoy such categorical properties.

Citations

• A Proof Theory for Profinite Modal Algebras
• Free algebras and coproducts in varieties of Gödel algebras
• Profiniteness, Monadicity and Universal Models in Modal Logic
• Stone duality, topological algebra, and recognition

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