Igor Arrieta

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math.GN2026

The lattice of smooth sublocales as a Bruns-Lakser completion

Igor Arrieta, Anna Laura Suarez

We characterise the frame morphisms $f : L \to M$ that lift to frame maps $f : S_{b} (L) \to S_{b} (M)$ , where $S_{b} (L)$ is the collection of joins of comp…

math.GN2026

Joins of closed sublocales are not always a coframe

Igor Arrieta

Given a locale $L$ , the collection $S_{c} (L)$ of joins of closed sublocales forms a frame--somewhat unexpectedly, as it is naturally embedded in the coframe of all sublocale…

math.GN2025

The DeMorganization of a locale

Igor Arrieta

In 2009, Caramello proved that each topos has a largest dense subtopos whose internal logic satisfies De Morgan law (also known as the law of the weak excluded middle). This findin…