We 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
Subj. Class.: Quantum groups, representations and corepresentations, amenability.
MSC 2000: Primary 46L05, 46L65. Secondary 22D10, 22D25, 43A07, 43A65, 58B32.
Keywords: quantum group, amenability.