English

Q-modules are Q-suplattices

Category Theory 2008-09-26 v1 Logic

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.

Keywords

Cite

@article{arxiv.0809.4343,
  title  = {Q-modules are Q-suplattices},
  author = {Isar Stubbe},
  journal= {arXiv preprint arXiv:0809.4343},
  year   = {2008}
}

Comments

12 pages

R2 v1 2026-06-21T11:24:02.177Z