An Equivalent of Algebraic $\Omega$-Categories
Received:March 31, 2016  Revised:December 14, 2016
Key Word: Quantitative domain   (algebraic) $\Omega$-category   bicomplete $\Omega$-category   equivalent category
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11531009; 11501343).
 Author Name Affiliation Na-na MA School of Statistics, Xi'an University of Finance and Economics, Shaanxi 710100, P. R. China Bin ZHAO School of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China
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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.