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A characterisation of the category of compact Hausdorff spaces

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arxiv 1808.09738 v4 pith:HU7LGBNK submitted 2018-08-29 math.CT math.GN

Vincenzo Marra , Luca Reggio This is my paper · ORCID
classification math.CTmath.GN
keywords categorycharacterisationcompacthausdorffspacesadmitsbooleancategorical
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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.

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  1. A universal characterization of standard Borel spaces

    math.LO 2019-08 accept novelty 8.0 of 10

    The category of standard Borel spaces is the initial countably complete Boolean countably extensive category, meaning it is freely generated by countable products, disjoint unions, and complementation.

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