Convergence and quantale-enriched categories
نویسندگان
1 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.
2 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.
doi
10.29252/cgasa.9.1.77چکیده
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.
