A characterisation of the category of compact Hausdorff spaces

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 a...

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Hlavní autoři: Marra, V, Reggio, L
Médium: Journal article
Jazyk:English
Vydáno: Theory and Applications of Categories 2020
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Shrnutí: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.