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Questions taking place in the category of locales, which is given by the opposite of the category of frames. Also appropriate for questions about pointless topology.

5 votes
2 answers
455 views

German translation of "locale" (from pointless topology)

Is there an established German translation of "locale"? The term appears mostly untranslated as "Locale"; a single time I've seen "Lokal". Where I'm located, we say "Örtlichkeit" or "Ort". Quoting th …
Ingo Blechschmidt's user avatar
12 votes
0 answers
421 views

What does the localic reflection of a classifying topos classify?

Let $\mathbb{T}$ be a geometric theory. Let $\mathrm{Set}[\mathbb{T}]$ be its classifying topos, such that geometric morphisms from any (cocomplete) topos $\mathcal{E}$ into $\mathrm{Set}[\mathbb{T}]$ …
Ingo Blechschmidt's user avatar
16 votes
Accepted

Locales as spaces of ideal/imaginary points

Yes, there is a general theory of locales as spaces of imaginary points. … The theory of classifying locales indeed allows you to construct spaces (locales) of things which aren't expected to exist, just by writing down the axioms of the hypothetical objects. …
Ingo Blechschmidt's user avatar