Part II is devoted to the development of logical frameworks for stable domains (dl-domains). There are many categories of domains with stable domains as objects and certain kinds of stable functions as morphisms. But they are scattered in the literature. To provide a background knowledge for the work of Part II, we give a survey of such categories (some of them are new) and indicates relationships among them (if possible). We actually present more categories than that are used later, so as to make this chapter a useful reference for categories of stable domains. These categories have been discovered with different motivations. Due to the lack of space we can only explain very briefly the motivations. However, we will try to provide enough information about the categories themselves, and leave it to interested readers to search into the relevant literatures listed in the bibliography for a complete account of applications of stable theories.
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