| 代数$Omega$-范畴的等价范畴 |
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| 引用本文： | 马娜娜,赵彬. 代数$Omega$-范畴的等价范畴[J]. 数学研究及应用, 2017, 37(2): 148-162 |
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| 作者姓名： | 马娜娜 赵彬 |
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| 作者单位： | 西安财经学院统计学院, 陕西 西安 710100,陕西师范大学数学与信息科学学院, 陕西 西安 710062 |
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| 基金项目： | 国家自然科学基金 (Grant Nos.11531009; 11501343). |
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| 摘 要： | 本文基于$Omega$-范畴研究了(连续) $mathcal{I}$-余万备$Omega$-范畴的一些性质. 我们给出了双完备$Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$mathcal{I}$-余万备$Omega$-范畴都是双完备$Omega$-范畴. 得到了代数$Omega$-范畴范畴等价于双完备$Omega$-范畴.
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| 关 键 词： | 量化domain (代数) $Omega$-范畴 双完备$Omega$-范畴 等价范畴 |
| 收稿时间： | 2016-03-31 |
| 修稿时间： | 2016-12-14 |
An Equivalent of Algebraic $Omega$-Categories |
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| Na-na MA and Bin ZHAO. An Equivalent of Algebraic $Omega$-Categories[J]. Journal of Mathematical Research with Applications, 2017, 37(2): 148-162 |
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| Authors: | Na-na MA and Bin ZHAO |
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| Affiliation: | School of Statistics, Xi''an University of Finance and Economics, Shaanxi 710100, P. R. China and School of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China |
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| Abstract: | In this paper, based on $Omega$-categories, some properties of (continuous) $mathcal{I}$-cocomplete $Omega$-categories are studied. Then, we introduce the concepts of bicomplete $Omega$-category and approximable bimodule, discuss their properties and we also show any $mathcal{I}$-cocomplete $Omega$-category is a bicomplete $Omega$-category. Finally, it is proved that the category of algebraic $Omega$-categories is equivalent to the category of bicomplete $Omega$-categories. |
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| Keywords: | Quantitative domain (algebraic) $Omega$-category bicomplete $Omega$-category equivalent category |
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