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

2013/12/04 by Olivia Caramello, Caramello, Olivia, Anna Carla Russo +1
Computer Science · Decision Sciences · Mathematics · #03G30 #06F20 #06F35 #18B25 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Logic (math.LO) #Logic, Reasoning, and Knowledge #math.CT #math.GR #math.LO #msc:03G30 #msc:06F20 #msc:06F35 #msc:18B25

paper · pdf · doi:10.48550/arxiv.1312.1272

29 pages

openalex publication_date 2013/12/04 · arxiv created 2014/04/22 · arxiv updated 2014/04/23 · openalex created_date 2016/10/21 · openalex updated_date 2026/07/28

Abstract

We show that the theory of MV-algebras is Morita-equivalent to that of abelian ℓ-groups with strong unit. This generalizes the well-known equivalence between the categories of set-based 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 sheaf-theoretic version of Mundici's equivalence and a bijective correspondence between the geometric theory extensions of the two theories.

Related

• On the equivalence between MV-algebras and l-groups with strong unit
• On the geometric theory of local MV-algebras
• Wide Morita contexts, relative injectivity and equivalence results
• Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective
• Morita theory in enriched context