2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62552We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this study, we also investigate the involved tensor C*-categories.46 pages, (some misprints corrected, a couple of remarks and a new reference added)Operator Algebras46L05, 46L65, 22D25text