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.