Would you consider this cheating:

A girl is dating a guy. She then starts to fall for another guy. She still stays in the relationship and doesn’t pursue the guy she’s writing about whatsoever. But she does write about him on her own time, knowing that she will never share them to anyone. She never did, until she broke up with her boyfriend and started dating the guy she was writing about.

I know this is complicated because technically the girl never shared her writings to anyone, including the guy she was writing about. However there’s also the argument that she did do an action that went against her partner, which is considered unfaithful. What do you guys think?