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John Iskra
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Disjoint Arrows in the category of locales

Call two arrows $f$ and $g$ disjoint if the pullback of $f$ by $g$ is the initial object. Here's my question: Does there exist a sublocale $j: J\to L$ which is not disjoint with any other (non-initial) sublocale of $L$, but which is disjoint with other non-initial arrows.

John Iskra
  • 404
  • 3
  • 10