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.
Keywords: Quantaloid, quantale, locale, ordered sheaf, module, centre, KZ doctrine
2000 MSC: 06F07, 18D05, 18D20
Theory and Applications of Categories,
Vol. 19, 2007,
No. 4, pp 50-60.
http://www.tac.mta.ca/tac/volumes/19/4/19-04.dvi
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http://www.tac.mta.ca/tac/volumes/19/4/19-04.pdf
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