Convergence and quantale-enriched categories

Document Type: Research Paper


1 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.

2 Polytechnic Institute of Coimbra, College of Management and Technology of Oliveira do Hospital, 3400-124 Oliveira do Hospital, Portugal; and Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal.


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.


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