Geodesic
Q-modules are Q-suplattices
Theory and applications of categories, CT2006, Tome 19 (2007), pp. 50-60

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 06F07, 18D05, 18D20
Keywords: Quantaloid, quantale, locale, ordered sheaf, module, centre, KZ doctrine 
@article{TAC_2007_19_a3,
     author = {Isar Stubbe},
     title = {Q-modules are {Q-suplattices}},
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     publisher = {mathdoc},
     volume = {19},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_19_a3/}
}
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Isar Stubbe. Q-modules are Q-suplattices. Theory and applications of categories, CT2006, Tome 19 (2007), pp. 50-60. http://geodesic.mathdoc.fr/item/TAC_2007_19_a3/