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Axiomatizing algebraically behaved categories of Hausdorff spaces. (English) Zbl 0796.18006

Seely, R. A. G. (ed.), Category theory 1991. Proceedings of an international summer category theory meeting, held in Montréal, Québec, Canada, June 23-30, 1991. Providence, RI: American Mathematical Society. CMS Conf. Proc. 13, 367-389 (1992).
This paper gives an internal characterization of categories of Hausdorff spaces such that the underlying set functor \(U\) is of descent type with dense units, i.e., \(U\) is right adjoint with dense units and has a full and faithful comparison functor into its Eilenberg-Moore category. This leads to characterizations of the category of Stone spaces and the category of compact Hausdorff spaces.
For the entire collection see [Zbl 0771.00047].

MSC:

18B30 Categories of topological spaces and continuous mappings (MSC2010)
18C20 Eilenberg-Moore and Kleisli constructions for monads
54B30 Categorical methods in general topology
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D30 Compactness
06E15 Stone spaces (Boolean spaces) and related structures
46L05 General theory of \(C^*\)-algebras
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