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Convergence and quantale-enriched categories

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arxiv 1705.08671 v1 pith:G3VTLL3N submitted 2017-05-24 math.CT

Dirk Hofmann , Carla Reis This is my paper · ORCID
classification math.CT
keywords categoriescompacthausdorfftopologycompletenessquantale-enrichedcategoricalcategory
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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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  1. Hausdorff coalgebras

    math.CT 2019-08 conditional novelty 6.0 of 10

    On quantale-enriched categories the Hausdorff functor has no terminal coalgebra, but on enriched compact Hausdorff spaces it preserves codirected limits, making categories of Hausdorff polynomial coalgebras complete.

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