Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/42771
Title: | Relative injectivity as cocompleteness for a class of distributors | Authors: | Clementino, Maria Manuel Hofmann, Dirk |
Keywords: | Quantale, V-category, monad, topological theory, distributor, Yoneda lemma, weighted colimit | Issue Date: | 2008 | Serial title, monograph or event: | Theory and Applications of Categories | Volume: | 12 | Issue: | 21 | Abstract: | Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces via adjunction, arXiv:math.CT/0804.0326] the construction of a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness and to show monadicity of the category of injective spaces and left adjoints over Set. In this paper we generalise these results, studying cocompleteness with respect to a given class of distributors. We show in particular that the description of several semantic domains presented in [M. Escardó and B. Flagg, Semantic domains, injective spaces and monads, Electronic Notes in Theoretical Computer Science 20 (1999)] can be translated into the V-enriched setting. | URI: | https://hdl.handle.net/10316/42771 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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21-12_CH09.pdf | 288.55 kB | Adobe PDF | View/Open |
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