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A characterisation of the category of compact Hausdorff spaces

Abstract:
We provide a characterisation of the category KH of compact Hausdorff spaces and continuous maps by means of categorical properties only. To this aim we introduce a notion of filtrality for coherent categories, relating certain lattices of subobjects to their Boolean centers. Our main result reads as follows: Up to equivalence, KH is the unique non-trivial well-pointed pretopos which is filtral and admits all set-indexed copowers of its terminal object.
Publication status:
Published
Peer review status:
Peer reviewed

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Publication website:
http://www.tac.mta.ca/tac/volumes/35/51/35-51abs.html

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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
Publisher:
Theory and Applications of Categories Publisher's website
Journal:
Theory and Applications of Categories Journal website
Volume:
35
Issue:
51
Pages:
1871-1906
Publication date:
2020-11-17
Acceptance date:
2020-11-06
ISSN:
1201-561X
Language:
English
Keywords:
Pubs id:
1157923
Local pid:
pubs:1157923
Deposit date:
2021-05-08

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