Baum-Schneider cohomology, Bivariant cycle cohomology, Bivariant cycle homology
See some files in Lipman folder for axioms for bivariant CTs.
Treat maybe also the possibly unrelated notion of birelative theories, see at least four such in the list of all CTs: Birelative homology, Bi-relative algebraic K-theory, Bi-relative topological cyclic homology, Bi-relative cyclic homology
nLab page on F60 Bivariant theories