Q-modules are Q-suplattices

Details Q-modules are Q-suplattices Q-modules are Q-suplattices

2008-09-25

arxiv.org/abs/0809.4343v1

Theory and Applications of Categories, Vol. 19, No. 4, 2007, pp. 50-60

Mathematics

Category Theory

12 pages

Scientific paper

It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing module-equivalence with sheaf-equivalence for quantaloids and using the notion of centre of a quantaloid, we refine a result of F. Borceux and E. Vitale.

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