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A characterisation of the category of compact Hausdorff spaces
Theory and applications of categories, Tome 35 (2020), pp. 1871-1906 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 18F60, 54B30
Keywords: compact Hausdorff spaces, coherent category, pretopos, filtrality, Stone spaces, exact completion 
@article{TAC_2020_35_a50,
     author = {Vincenzo Marra and Luca Reggio},
     title = {A characterisation of the category of compact {Hausdorff} spaces},
     journal = {Theory and applications of categories},
     pages = {1871--1906},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a50/}
}
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Vincenzo Marra; Luca Reggio. A characterisation of the category of compact Hausdorff spaces. Theory and applications of categories, Tome 35 (2020), pp. 1871-1906. http://geodesic.mathdoc.fr/item/TAC_2020_35_a50/