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• W2024873396 abstract "Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $omega $-categories. To apply these general ideas we introduce Wand’s ${bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott’s universal domain method can be included too." @default.
• W2024873396 created "2016-06-24" @default.
• W2024873396 creator A5061751667 @default.
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• W2024873396 date "1982-11-01" @default.
• W2024873396 modified "2023-09-29" @default.
• W2024873396 title "The Category-Theoretic Solution of Recursive Domain Equations" @default.
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• W2024873396 doi "https://doi.org/10.1137/0211062" @default.
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