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.

A characterisation of the category of compact Hausdorff spaces / V. Marra, L. Reggio. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 35:51(2020), pp. 1871-1906.

A characterisation of the category of compact Hausdorff spaces

Marra V.;
2020

Abstract

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.
Coherent category; compact Hausdorff spaces; Exact completion; Filtrality; Pretopos; Stone spaces
Settore MAT/01 - Logica Matematica
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
THEORY AND APPLICATIONS OF CATEGORIES
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/808736
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