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Journal Articles Theory and Applications of Categories Year : 2007

Q-modules are Q-suplattices

Abstract

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.

Dates and versions

hal-03606832 , version 1 (12-03-2022)

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Isar Stubbe. Q-modules are Q-suplattices. Theory and Applications of Categories, 2007, 19 (4), pp.50-60. ⟨hal-03606832⟩

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UNIV-LITTORAL
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