Geodesic
Cauchy completion of fuzzy quasi-uniform spaces
Filomat, Tome 35 (2021) no. 12, p. 3983

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DOI

In this paper, we study the completion of fuzzy quasi-uniform spaces from a categorical point of view. Firstly, we introduce the concept of prorelations and describe fuzzy quasi-uniform spaces as enriched categories. Then we construct the Yoneda embedding in fuzzy quasi-uniform spaces through promodules, and prove the validness of Yoneda Lemma for right adjoint promodules. Finally, we study the Cauchy completion of fuzzy quasi-uniform spaces by the Yoneda embedding. We show that the inclusion functor from the category of T 0 separated complete fuzzy quasi-uniform spaces to the category of fuzzy quasi-uniform spaces has a left adjoint functor. The monad related to this adjunction is just the T 0 completion monad of fuzzy quasi-uniform spaces
DOI : 10.2298/FIL2112983W
Classification : 54B30, 54A40, 18D20
Keywords: Cauchy completion, promodule, Yoneda embedding, prorelation, fuzzy quasi-uniform space 
Yongchao Wang; Yueli Yue. Cauchy completion of fuzzy quasi-uniform spaces. Filomat, Tome 35 (2021) no. 12, p. 3983 . doi: 10.2298/FIL2112983W
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     author = {Yongchao Wang and Yueli Yue},
     title = {Cauchy completion of fuzzy quasi-uniform spaces},
     journal = {Filomat},
     pages = {3983 },
     year = {2021},
     volume = {35},
     number = {12},
     doi = {10.2298/FIL2112983W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2112983W/}
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