Let us write            l    G    u    f          for the category whose objects are lattice-ordered abelian groups ( l -groups for short) with a strong unit and finite prime spectrum endowed with a collection of Archimedean elements, one for each prime  l -ideal, which satisfy certain properties, and whose arrows are  l   -homomorphisms with additional structure. In this paper we show that a functor which assigns to each object            (  A  ,    u    ˆ    )  ∈  l    G    u    f          the prime spectrum of  A   , and to each arrow            f  :  (  A  ,    u    ˆ    )  →  (  B  ,    v    ˆ    )  ∈  l    G    u    f          the naturally induced  p -morphism, has a left adjoint.
['José Luis Castiglioni', 'Hernán Javier San Martín']
The left adjoint of Spec from a category of lattice-ordered groups