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Abstract: In the context of categorical topology, more precisely that of T-categoriesHofmann, 2007, we define the notion of T-colimit as a particular colimit in aV-category. A complete and cocomplete V-category in which limits distributeover T-colimits, is to be thought of as the generalisation of a co-frame tothis categorical level. We explain some ideas on a T-categorical version of-Stone duality-, and show that Cauchy completeness of a T-category is preciselyits sobriety.



Author: Dirk Hofmann, Isar Stubbe

Source: https://arxiv.org/



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