The relative tensor product and a minimal fiber product in the setting of $C^{*}$-algebras

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.