  Generalising the well-known correspondence between two-sided adjunctions and
Frobenius algebras, we establish a one-to-one correspondence between local
adjunctions of C*-correspondences, as defined and studied in prior work with P.
Clare and N. Higson; and Frobenius C*-algebras, a natural C*-algebraic
adaptation of the standard notion of Frobenius algebras that we introduce here.
