代数$\Omega$-范畴的等价范畴

An Equivalent of Algebraic $\Omega$-Categories

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

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.