# General affine adjunctions, Nullstellensätze, and dualities

@article{Caramello2014GeneralAA, title={General affine adjunctions, Nullstellens{\"a}tze, and dualities}, author={Olivia Caramello and V. Marra and L. Spada}, journal={arXiv: Category Theory}, year={2014} }

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

2 Citations

MV-algebras, infinite dimensional polyhedra, and natural dualities

- Mathematics, Computer Science
- 2017

- 4
- PDF

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 53 REFERENCES

Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras

- Mathematics, Computer Science
- 2013

- 25
- PDF

The Morita-equivalence between MV-algebras and lattice-ordered abelian groups with strong unit

- Mathematics
- 2015

- 12

The Morita-equivalence between MV-algebras and abelian $\ell$-groups with strong unit

- Mathematics
- 2013

- 4
- PDF

Lattice-Ordered Abelian Groups and Perfect MV-Algebras: a Topos-Theoretic Perspective

- Computer Science, Mathematics
- 2016

- 5
- PDF