Elementary characterisation of small quantaloids of closed cribles - Archive ouverte HAL Access content directly
Journal Articles Journal of Pure and Applied Algebra Year : 2012

Elementary characterisation of small quantaloids of closed cribles

Abstract

Each small site (C,J) determines a small quantaloid of closed cribles R(C,J). We prove that a small quantaloid Q is equivalent to R(C,J) for some small site (C,J) if and only if there exists a (necessarily subcanonical) Grothendieck topology J on the category Map(Q) of left adjoints in Q such that Q=R(Map(Q),J), if and only if Q is locally localic, map- discrete, weakly tabular and weakly modular. If moreover coreflexives split in Q, then the topology J on Map(Q) is the canonical topology.

Dates and versions

hal-03606337 , version 1 (11-03-2022)

Identifiers

Cite

Hans Heymans, Isar Stubbe. Elementary characterisation of small quantaloids of closed cribles. Journal of Pure and Applied Algebra, 2012, 216 (8-9), pp.1952-1960. ⟨10.1016/j.jpaa.2012.02.032⟩. ⟨hal-03606337⟩

Altmetric

Share

Gmail Facebook X LinkedIn More