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Journal Articles Cahiers de topologie et géométrie différentielle catégoriques Year : 2010

'Hausdorff distance' via conical cocompletion

Abstract

In the context of quantaloid-enriched categories, we explain how each saturated class of weights defines, and is defined by, an essentially unique full sub-KZ-doctrine of the free cocompletion KZ-doctrine. The KZ-doctrines which arise as full sub-KZ-doctrines of the free cocompletion, are characterised by two simple "fully faithfulness" conditions. Conical weights form a saturated class, and the corresponding KZ-doctrine is precisely (the generalisation to quantaloid-enriched categories of) the Hausdorff doctrine of [Akhvlediani et al., 2009].

Dates and versions

hal-03606831 , version 1 (12-03-2022)

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Cite

Isar Stubbe. 'Hausdorff distance' via conical cocompletion. Cahiers de topologie et géométrie différentielle catégoriques, 2010, 51 (1), pp.51-76. ⟨hal-03606831⟩

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