| An Equivalent of Algebraic $\Omega$-Categories |
| Received:March 31, 2016 Revised:December 14, 2016 |
| Key Words:
Quantitative domain (algebraic) $\Omega$-category bicomplete $\Omega$-category equivalent category
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11531009; 11501343). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.02.003 |
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