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arXiv · 1705.08671

Convergence and quantale-enriched categories

Dirk Hofmann·Carla Reis
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Abstract

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 $\mathcal{V}$-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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Dirk Hofmann, Carla Reis. 2017-05-24. Convergence and quantale-enriched categories. https://arxiv.org/abs/1705.08671

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