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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.
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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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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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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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 …
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