The left adjoint of Spec from a category of lattice-ordered groups

J.L. CASTIGLIONI; H.J. SAN MARTÍN

JOURNAL OF APPLIED LOGIC

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2016 vol. 15 p. 1 - 12

1570-8683

Let us write lGfu 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 Archimedeanelements, 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) ?¸  lGfu the prime spectrum of A, and to each arrow f: :(A, u) ?¨(B, v) ?¸  lGfu the naturally induced p-morphism, has a left adjoint.