Questions tagged [locales]

For questions about locales, a generalization of topological spaces which need not have points. Their study is called pointless topology.

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1answer
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Do products preserve colimits in the category of locales?

Does the functor $X\times-:\mathbf{Loc}\to\mathbf{Loc}$ preserve small colimits for all locales $X$? The reason that I'm interested in this question is that the same property fails in the category of ...
6
votes
1answer
122 views

The etale locale of a sheaf?

It's well-known that sheaves over a topological space are equivalent to etale spaces over the same space. Now if we replace "topological space" by "locale", we can still define sheaves over a locale, ...
6
votes
2answers
388 views

Info on the locale of surjections from the Natural Numbers to the Real Numbers

On the nlab page for locales, it states that there is locale for the surjections from the Naturals to the Reals. This locale has no points (i.e. elements), since there are no such surjections, but the ...
2
votes
1answer
149 views

Is there a classifying topos for locales?

Is there a Grothendieck topos $F$ such that, for any Grothendieck topos $E$, the category of geometric morphisms $$E\rightarrow F$$ is equivalent to the category of locales internal to $F$? I suspect ...