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arXiv · 1004.0160

Stone duality for topological theories

Dirk Hofmann·Isar Stubbe
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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.

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Dirk Hofmann, Isar Stubbe. 2010-04-01. Stone duality for topological theories. https://arxiv.org/abs/1004.0160

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