Defining Symmetric vs Asymmetric cryptosystems
Your definition only covers symmetric encryption since the same "index" $k$ is used in $T_k$ and $T^{-1}_k$ (i.e., encryption and decryption use the same key)

If you want to give a generic definition that covers both types of encryption, you could say that the transformations are $T_k$ and $T^{-1}_{k'}$ and that in the case of symmetric encryption $k'=k$.