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].Comment: Minor change
