We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

There are categories of ‘spaces' that are not categories of locales

Formal Metadata

Title
There are categories of ‘spaces' that are not categories of locales
Title of Series
Part Number
22
Number of Parts
28
Author
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
We described a short list of categorical axioms that make a category behave like the category of locales. In summary the axioms assert that the category has an object that behaves like the Sierpnski space and this object is double exponentiable. A number of the usual results of locale theory can be derived using the axioms: the (weakly) closed subgroup theorem proved, closed and proper surjection are of eective descent, parallel theories of discrete and compact Hausdor spaces emerge. An example is given of a category that satises the axioms but which is not the category of locales for any topos. We show how to embed the category of elementary toposes into the category whose objects are categories that satisfy the axioms.