Report
Categorical Extension of Dualities: From Stone to de Vries and Beyond, II
| العنوان: | Categorical Extension of Dualities: From Stone to de Vries and Beyond, II |
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| المؤلفون: | Dimov, G., Ivanova-Dimova, E., Tholen, W. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, Mathematics - General Topology, 54D45, 18A40, 18B30, 54E05, 54C10, 54G05, 06E15, 03G05 |
| الوصف: | Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category $\bf LKHaus$ of locally compact Hausdorff spaces and continuous maps, with the dual equivalence extending a Stone-type duality for the category of extremally disconnected locally compact Hausdorff spaces and continuous maps. The new category is then shown to be isomorphic to the category $\bf CLCA$ of complete local contact algebras and suitable morphisms. Thereby, a new proof is presented for the equivalence ${\bf LKHaus}\simeq{\bf CLCA}^{\rm op}$ that was obtained by the first author more than a decade ago. Unlike the morphisms of $\bf CLCA$, the morphisms of the new category and their composition law are very natural and easy to handle. Comment: 32 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.07172 |
| رقم الانضمام: | edsarx.2109.07172 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |