Over the past few decades, the classification results for C*-algebras have been built on those of morphisms. In the recent work of Carrión, Gabe, Schafhauser, Tikuisis and White, they recaptured the classification theorem for a large class of simple Z-stable C*-algebras by classifying maps into such C*-algebras. Following their abstract classification framework, we go beyond the range of currently existing classification results.
For instance, as part of our results, uniqueness theorems for maps into II1-factors and ultraproducts of matrices are obtained, where codomain C*-algebras are either not known to admit Z-stability or are known to lack Z-stability.
