| 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 |
| 代数$\Omega$-范畴的等价范畴 |
| An Equivalent of Algebraic $\Omega$-Categories |
| 投稿时间：2016-03-31 修订日期：2016-12-14 |
| DOI：10.3770/j.issn:2095-2651.2017.02.003 |
| 中文关键词: 量化domain (代数) $\Omega$-范畴 双完备$\Omega$-范畴 等价范畴 |
| 英文关键词:Quantitative domain (algebraic) $\Omega$-category bicomplete $\Omega$-category equivalent category |
| 基金项目:国家自然科学基金 (Grant Nos.11531009; 11501343). |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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