Classification of homomorphisms into simple Z-stable C⁎-algebras

We classify unital monomorphisms into certain simple Z-stable C⁎-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C⁎-algebra, or any unital simple separable nuclear Z-stable C⁎-algebra satisfying the UCT such that C⊗B is of tracial rank zero for a UHF algebra B. The target algebra A is allowed to be any unital simple separable Z-stable C⁎-algebra such that A⊗B has tracial rank zero for a UHF algebra B, or any unital simple separable exact Z-stable C⁎-algebra whose projections separate traces and whose extremal traces are finitely many.