General affine adjunctions, Nullstellensätze, and dualities

  title={General affine adjunctions, Nullstellens{\"a}tze, and dualities},
  author={Olivia Caramello and V. Marra and L. Spada},
  journal={arXiv: Category Theory},
  • Olivia Caramello, V. Marra, L. Spada
  • Published 2014
  • Mathematics
  • arXiv: Category Theory
  • 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… CONTINUE READING

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