Finite coproducts, coregularity and coexactness for profinite interior algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918142189502464 |
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| author | De Berardinis, Matteo |
| author_facet | De Berardinis, Matteo |
| contents | 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 $\textbf{Set}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite coproducts, coregularity and coexactness for profinite interior algebras De Berardinis, Matteo Logic Category Theory 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 $\textbf{Set}$. 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. |
| title | Finite coproducts, coregularity and coexactness for profinite interior algebras |
| topic | Logic Category Theory |
| url | https://arxiv.org/abs/2509.13058 |