Given a small quantaloid Q with a set of objects Q_0, it is proved that complete skeletal Q-categories, completely distributive skeletal Q-categories, and Q-powersets of Q-typed sets are all monadic over athe slice category of Set over Q_0.
Keywords: Quantaloid, Q-category, complete Q-category, completely distributive Q-category, Q-powerset, Eilenberg-Moore algebra, monadicity
2010 MSC: 18A40, 18C20, 18D20, 18D35
Theory and Applications of Categories, Vol. 30, 2015, No. 21, pp 751-774.