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.
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