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The Collaborative International Dictionary
Hyperdulia

Hyperdulia \Hy`per*du*li"a\, n. [Pref. hyper- + dulia: cf. F. hyperdulie.] (R. C. Ch.) Veneration or worship given to the Virgin Mary as the most exalted of mere creatures; higher veneration than dulia.
--Addis & Arnold.

Wiktionary
hyperdulia

n. (context Roman Catholicism English) A level of veneration higher than dulia but less than latria, properly given to the Virgin Mary.