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Journal Articles Topology and its Applications Year : 2011

Stone duality for topological theories

Abstract

In the context of categorical topology, more precisely that of T-categories [Hofmann, 2007], we define the notion of T-colimit as a particular colimit in a V-category. A complete and cocomplete V-category in which limits distribute over T-colimits, is to be thought of as the generalisation of a (co-)frame to this categorical level. We explain some ideas on a T-categorical version of "Stone duality", and show that Cauchy completeness of a T-category is precisely its sobriety.

Dates and versions

hal-03606829 , version 1 (12-03-2022)

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Dirk Hofmann, Isar Stubbe. Stone duality for topological theories. Topology and its Applications, 2011, 158 (7), pp.913-925. ⟨10.1016/j.topol.2011.01.010⟩. ⟨hal-03606829⟩
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