A representation theorem for integral rigs and its applications to residuated lattices
Jorge Castiglioni, M. Menni, W. J. Zuluaga Botero · arXiv (Cornell University) · 2015
We prove that every integral rig in Sets is (functorially) the rig of global sections of a sheaf of really local integral rigs. We also show that this representation result may be lifted to residuated integral rigs and then restricted to varieties of these. In particular, as a corollary, we obtain a representation theorem for pre-linear residuated join-semilattices in terms of totally ordered fibers. The restriction of this result to the level of MV-algebras coincides with the Dubuc-Poveda representation theorem.