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Results tagged with locales
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user 2733
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.
6
votes
Definition of Category of Locales
For example, in Johnstone's book you will find definitions of locally compact locales and of open (continous) maps. …
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3
votes
Coequalizers in the category of algebras of the double power locale monad
The objects of the category $\mathbf{Dcpo}'$ in my notation above
(which is the opposite of the category of algebras in Chris's question)
are called localic locales by Steve Vickers and colocales by me … The latter relates continuous frames to locally compact locales,
so any continuous frame is a colocale. …
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1
vote
The field structure on the locale of real numbers
Richard Dedekind's original paper does not include a construction of multiplication.
In The Dedekind Reals in Abstract Stone Duality, Andrej Bauer and I go into considerable detail about all of the to …
- 8,481
15
votes
Localic locales? Towards very pointless spaces by iterated internalization.
Can we do something similar taking $S$ to be the category of locales, to get back to David's question? Indeed, Steve Vickers has studied this,
using his double powerlocale monad. … We therefore have the categories $L$ of locales and $C$ of colocales, where $C^{op}$ is monadic over $L$, but they are not equivalent. …
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4
votes
Status of the fundamental theorem of algebra for the locale of real numbers
I can see two issues of non-constructivity here, but I feel that they are both noise rather than central to the mathematics:
The leading coefficient of the polynomial could fail to be apart from zero, …
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