## Tagged Questions

1answer
58 views

### On the openness of the map X^I -> X * X.

Hello ! Let $X$ be a locale or a topological spaces. $I$ denote the unit interval of the real numbers, and $X^I$ the space of function from $I$ to $X$ (The locale exponential if \$ …
0answers
211 views

### Are $\infty$-topoi determined by their localic points ?

Hello ! If $T$ is an infinity topos, then you can consider the infinity category of geometric morphism from $Sh_{\infty}(\mathcal{L})$ to $T$ for any locale $\mathcal{L}$. This as …
0answers
484 views

### $\infty$-topos and localic $\infty$-groupoids ?

Hello ! It's known that every classical (Grothendieck) topos is equivalent to the topos of sheaves on a localic groupoid (a groupoid in the category of locales). For the record, …
2answers
226 views

### Given a Grothendieck topos, what does its localic groupoid look like?  [closed]

Possible Duplicate: Toposes (topoi) as classifying toposes of groupoids For example, if a topos E is the object classifier, or the preseaf topos on a small category C, is …
3answers
1k views

### Locales and Topology.

As someone more used to point-set topology, who is unfamiliar with the inner workings of lattice theory, I am looking to learn about the localic interpretation of topology, of whic …
0answers
51 views

### Intersection of open sublocale of a compact regular locale ?

Hello ! It's well know that any sublocale of regular locale is the intersection of a familly of open sublocale. Hence if $X$ is a regular locale, the map which to a sublocal \$Y \s …
1answer
275 views

### Counterexemple to Urysohn’s lemma in a topos without denombrable choice ?

Hello ! The Urysohn's Lemma assert that in every topological spaces which is normal two closed subset may be separated by a real valued function. It's proof use axiom of countable …
0answers
95 views

### surjection of localic infinity toposes?

Hello! Is there a simple 'topological' condition to detect whenever a morphism of locales $f : X \rightarrow Y$ induces a surjection of infinity-toposes \$f : \mathrm{Sh}_{\infty} …
0answers
424 views

### Which complete Boolean algebras arise as the algebras of projections of commutative von Neumann algebras?

Projections in an arbitrary commutative von Neumann algebra form a complete Boolean algebra. Moreover, a morphism of commutative von Neumann algebras induces a continuous morphism …
3answers
537 views

### Localic locales?  Towards very pointless spaces by iterated internalization.

One can think of locales as (generalizations of) topological spaces which don't necessary have (enough) points. Of course when one studies locales, one "actually" studies frames, …
5answers
854 views

### Stone Spaces, Locales, and Topoi for the (relative) beginner

I am currently reading Vickers' text "topology via logic" and Peter Johnstone's "stone spaces", and I understand the material in both of these texts to pertain directly to construc …
1answer
306 views

### Do strict pro-sets embed in locales?

It is well-known that the category of profinite groups (by which I mean Pro(FiniteGroups), i.e. the category of formal cofiltered limits of finite groups) is equivalent to a full s …
2answers
382 views

### Definition of Category of Locales

In the wikipedia entry for 'frames and locales', pains are taken to distinguish between the category of locales - defined to be the opposite of the category of frames - and the cat …
1answer
160 views

### Strong monics in the category of locales

Are there non-regular strong monics in the category of locales?
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