A characterisation of the category of compact Hausdorff spaces

Vincenzo Marra and Luca Reggio

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.

Keywords: compact Hausdorff spaces, coherent category, pretopos, filtrality, Stone spaces, exact completion

2020 MSC: 18F60, 54B30

Theory and Applications of Categories, Vol. 35, 2020, No. 51, pp 1871-1906.

Published 2020-11-17.


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