A representation theorem for integral rigs and its applications to residuated lattices

J. L. Castiglioni; M. Menni; W. J. Zuluaga Botero

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arXiv · 1510.06332

A representation theorem for integral rigs and its applications to residuated lattices

J. L. Castiglioni·M. Menni·W. J. Zuluaga Botero

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Abstract

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.

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BibTeX RIS

J. L. Castiglioni, M. Menni, W. J. Zuluaga Botero. 2015-10-20. A representation theorem for integral rigs and its applications to residuated lattices. https://arxiv.org/abs/1510.06332

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