Completely distributive enriched categories are not always continuous
Hongliang Lai, Dexue Zhang · Theory and applications of categories · 2020
In contrast to the fact that every completely distributive lattice is necessarily continuous in the sense of Scott, it is shown that complete distributivity of a category enriched over the closed category obtained by endowing the unit interval with a continuous t-norm does not imply its continuity in general.Necessary and sufficient conditions for the implication are presented.We would like to thank the support of the National Natural Science Foundation of China (No. 11771310 and No. 11871358).