Completely distributive enriched categories are not always continuous
Category Theory
2020-01-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1908.01106,
title = {Completely distributive enriched categories are not always continuous},
author = {Hongliang Lai and Dexue Zhang},
journal= {arXiv preprint arXiv:1908.01106},
year = {2020}
}
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23 pages