Ideally Exact Categories, Varieties of Universal Algebras and Multi-valued Logics
(2026) IPMU 2026 - Information Processing and Management of Uncertainty in Knowledge-Based Systems — Location: Rome, Italy (15.June.2026)
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- (en) We study the notions of coherent and ideal actions in the setting of ideally exact varieties of universal algebras. We prove that, if V is a semi-abelian variety and U is obtained from V by freely adding nullary operations together with suitable identities, then the ideally exact context determined by the associated free-forgetful monadic adjunction with cartesian unit has a good theory of actions if and only i f a compatibility condition between coherent actions and the added identities is satisfied. Our setting applies in particular to certain categories of interest in algebraic logic, including MV-algebras and product algebras.
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Mancini, M., & Piazza, F. (2026). Ideally Exact Categories, Varieties of Universal Algebras and Multi-valued Logics. In Manuel Mancini, Federica Piazza (ed.), Ideally Exact Categories, Varieties of Universal Algebras and Multi-valued Logics (pp. 262-276). Springer Cham. https://doi.org/10.1007/978-3-032-28997-1_19