Simplicial geometry of unital lattice-ordered abelian groups

2012/02/21 by Cabrer, Leonardo Manuel
#05E45 (Secondary) #06F20 (Primary) #18A35 #18B30 #52B11 #52B20 #55U05 #55U10 #57Q05 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1202.5947

Abstract

By an ℓ-group G we mean a lattice-ordered abelian group. This paper is concerned with the category \FP of finitely presented \it unital ℓ-groups, those ℓ-groups having a distinguished order-unit u. Using the duality between \FP the category of rational polyhedra, we will provide (i) a construction of finite limits and co-limits in \FP; (ii) a Cantor-Bernstein-Schröder theorem for finitely presented unital ℓ-groups; (iii) a geometrical characterization of finitely generated subalgebras of free objects of \FP.

Related

• Rational Simplicial geometry and projective unital lattice-ordered abelian groups
• Classification of finitely generated lattice-ordered abelian groups with order-unit
• Finitely presented lattice-ordered abelian groups with order-unit
• Rational polyhedra and projective lattice-ordered abelian groups with order unit
• A Stone-Weierstrass theorem for MV-algebras and unital ℓ-groups