'Hausdorff distance' via conical cocompletion

Details 'Hausdorff distance' via conical cocompletion 'Hausdorff distance' via conical cocompletion

2009-03-16

arxiv.org/abs/0903.2722v2

Mathematics

Category Theory

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Scientific paper

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].

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