Localizability of the nonzero filter in a quantale

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Let QQ be a quantale with bottom element 00, and let mid0 mid 0 denote the property of being nonzero. Let mid0 mid 0 be the corresponding filter over QQ.

Nonzero-filter localizability conjecture. The filter mid0 mid 0 is localizable over QQ.

This would remove the reducedness hypothesis from the cited theorem on conormal dense filters. The source presents the assertion as a question, and no resolution is supplied.

References

Primary source

Bangzheng Li and Yichen Xiao, “Commutative Quantale and Localization”, arXiv:2508.02991 (2025).

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