arxiv: 1004.0160 · v2 · pith:KBC6AJWYnew · submitted 2010-04-01 · 🧮 math.CT · math.GN

Stone duality for topological theories

Dirk Hofmann , Isar Stubbe This is my paper

classification 🧮 math.CT math.GN

keywords categoricaldualitypreciselystonev-categorycauchycocompletecolimit

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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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Stone duality for topological theories

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