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A characterisation of the category of compact Hausdorff spaces

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I will present a categorical characterisation of the category KH of compact Hausdorff spaces and continuous maps. To this end, a notion of ‘filtrality’ for coherent categories is introduced, whereby certain lattices of subobjects are related to their Boolean centers. Our main result reads as follows: Up to equivalence, KH is the unique non-trivial well-pointed pretopos that is filtral and admits all set-indexed copowers of its terminal object. This is joint work with Vincenzo Marra (TAC, Vol.35, No.51, pp.1871-1906, 2020).

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This talk is part of the Category Theory Seminar series.

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