Geodesic
Completely distributive enriched categories are not always continuous
Theory and applications of categories, Tome 35 (2020), pp. 64-88
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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.

Publié le :
Classification : 18B35, 18D20, 06D10, 06F07
Keywords: Enriched category, continuous t-norm, forward Cauchy weight, distributive law, completely distributive quantale-enriched category, continuous quantale-enriched category 
@article{TAC_2020_35_a2,
     author = {Hongliang Lai and Dexue Zhang},
     title = {Completely distributive enriched categories  are not always continuous},
     journal = {Theory and applications of categories},
     pages = {64--88},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a2/}
}
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Hongliang Lai; Dexue Zhang. Completely distributive enriched categories  are not always continuous. Theory and applications of categories, Tome 35 (2020), pp. 64-88. http://geodesic.mathdoc.fr/item/TAC_2020_35_a2/