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...
| Egile Nagusiak: | , |
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| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
Theory and Applications of Categories
2020
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| Gaia: | 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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