We introduce and investigate a category-theoretic abstraction of the standard “system-solution” adjunction in affine algebraic geometry. We then look further into these geometric adjunctions at different levels of generality, from syntactic categories to (possibly infinitary) equational classes of algebras. In doing so, we discuss the relationships between the dualities induced by our framework and the well-established theory of concrete dual adjunctions. In the context of general algebra we prove an analogue of Hilbert's Nullstellensatz, thereby achieving a complete characterisation of the fixed points on the algebraic side of the adjunction.

General affine adjunctions, Nullstellensätze, and dualities / O. Caramello, V. Marra, L. Spada. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 225:1(2021), pp. 106470.1-106470.33. [10.1016/j.jpaa.2020.106470]

General affine adjunctions, Nullstellensätze, and dualities

Marra V.;
2021

Abstract

We introduce and investigate a category-theoretic abstraction of the standard “system-solution” adjunction in affine algebraic geometry. We then look further into these geometric adjunctions at different levels of generality, from syntactic categories to (possibly infinitary) equational classes of algebras. In doing so, we discuss the relationships between the dualities induced by our framework and the well-established theory of concrete dual adjunctions. In the context of general algebra we prove an analogue of Hilbert's Nullstellensatz, thereby achieving a complete characterisation of the fixed points on the algebraic side of the adjunction.
Ordered abelian-grous; MV-algebras
Settore MAT/02 - Algebra
Settore MAT/01 - Logica Matematica
JOURNAL OF PURE AND APPLIED ALGEBRA
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/781885
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