Extending Chang's construction to the category of m-zeroids and some category containing the category of abelian \(\ell\)-groups with strong unit. (Q2439669)

In 1958 \textit{C. C. Chang} [Trans. Am. Math. Soc. 87, 55-56 (1958; Zbl 0085.24402)] introduced MV-algebras to prove the completeness of the Łukasiewicz axioms. The proof was achieved in 1959, using the following key fact: every MV-algebra \((A,0,\neg,\oplus)\) is obtainable from the unit interval \([0,p]\) of a totally ordered abelian group \(G\), with \(p\geq 0\), \(\neg x=p-x\) and \(x\oplus y=\min(p,x+y)\). Extending this result, in 1986 the present reviewer constructed a categorical equivalence \(\Gamma\) between MV-algebras and lattice-ordered abelian groups with a distinguished strong order unit, for short unital \(l\)-groups. In the paper under review it is shown that for no extension \(E\) of the category of unital \(l\)-groups there is an extension of the \(\Gamma\) functor from \(E\) to \(m\)-zeroids. \{Reviewer's remark: The author is unaware of the original paper where the \(\Gamma\) functor was introduced, namely \textit{D. Mundici} [J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)].\}