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.
A characterisation of the category of compact Hausdorff spaces / V. Marra, L. Reggio. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 35:51(2020), pp. 1871-1906.
A characterisation of the category of compact Hausdorff spaces
V. Marra;
2020
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.
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