  We introduce a relative tensor product of $C^{*}$-modules and a spatial fiber
product of $C^{*}$-algebras that are analogues of Connes' fusion of
correspondences and the fiber product of von Neumann algebras introduced by
Sauvageot, respectively, and study their categorical properties. These
constructions form the basis for our approach to quantum groupoids in the
setting of $C^{*}$-algebras that is published separately.
