On the completion monad via the Yoneda embedding in quasi-uniform spaces
نویسندگان
چکیده
منابع مشابه
On the Completion Monad via the Yoneda Embedding in Quasi-uniform Spaces
Making use of the presentation of quasi-uniform spaces as generalised enriched categories, and employing in particular the calculus of modules, we define the Yoneda embedding, prove a (weak) Yoneda Lemma, and apply them to describe the Cauchy completion monad for quasi-uniform spaces.
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Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special...
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Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...
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Received We show how to solve the word problem for simply typed-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. The formal setting for these results is P-category theory, a version of ordinary category theory where each hom-set is equipped with a partial equivalence relation. The part of P-category theory we develop here is constructive and thus...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.01.026