The Moritaequivalence between MValgebras and abelian $\ell$groups with strong unit
Abstract
We show that the theory of MValgebras is Moritaequivalent to that of abelian $\ell$groups with strong unit. This generalizes the wellknown equivalence between the categories of setbased models of the two theories established by D. Mundici in 1986, and allows to transfer properties and results across them by using the methods of topos theory. We discuss several applications, including a sheaftheoretic version of Mundici's equivalence and a bijective correspondence between the geometric theory extensions of the two theories.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 arXiv:
 arXiv:1312.1272
 Bibcode:
 2013arXiv1312.1272C
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Group Theory;
 Mathematics  Logic;
 06F20;
 06F35;
 18B25;
 03G30
 EPrint:
 29 pages