Abstract
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.
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