Completely distributive enriched categories are not always continuous

Hongliang Lai and Dexue Zhang

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: Enriched category, continuous t-norm, forward Cauchy weight, distributive law, completely distributive quantale-enriched category, continuous quantale-enriched category

2010 MSC: 18B35, 18D20, 06D10, 06F07

Theory and Applications of Categories, Vol. 35, 2020, No. 3, pp 64-88.

Published 2020-01-24.

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