A general framework for geometric dualities for varieties of algebras

4 pages•Published: July 28, 2014

Abstract

We set up a framework that subsumes many important dualities in mathematics (Birkhoff, Stone, Priestly, Baker-Beynon, etc.) as well as the classical correspondence between polynomial ideals and affine varieties in algebraic geometry. Our main theorems provide a generalisation of Hilbert's Nullstellensatz to any (possibly infinitary) variety of algebras. The common core of the above dualities becomes then clearly visible and sets the basis to a canonical method to seek for a geometric dual to any given variety of algebras.

Keyphrases: algebraic geometry, categorical adjunction, galois adjunction, hilbert nullstellensatz, stone dualities, topological duality, universal algebra

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 213-216.

Links:	https://easychair.org/publications/paper/CcJ
	https://doi.org/10.29007/3bk1

BibTeX entry

@inproceedings{TACL2013:general_framework_geometric_dualities,
  author    = {Luca Spada},
  title     = {A general framework for geometric dualities for varieties of algebras},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/CcJ},
  doi       = {10.29007/3bk1},
  pages     = {213-216},
  year      = {2014}}

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