We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of Picard group a continuous-trace C⁎-algebra (1981) [14] can be applied to arbitrary C⁎-algebras, via an algebraic argument with Haagerup tensor product. put this result into context descent theory identifying categories data over C⁎-algebras comodules C⁎-coalgebras, giving Hilbert-module version ...