%0 Journal Article %T Convergence and quantale-enriched categories %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Hofmann, Dirk %A D. Reis, Carla %D 2018 %\ 07/01/2018 %V 9 %N 1 %P 77-138 %! Convergence and quantale-enriched categories %K Ordered compact Hausdorff space %K metric space %K approach space %K sober space %K Cauchy completness %K quantale-enriched category %R 10.29252/cgasa.9.1.77 %X Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $\V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) codirected completeness of the underlying quantale enriched category. %U https://cgasa.sbu.ac.ir/article_58262_bab8553989f148c1daf7939ffd5b9f4d.pdf