Hi, I think one can argue that rotation by 350º and by -10º are the same morphism in **Vect**. They are equal element-wise ("extensionally"), so that would leave us only with one inverse. Another option without this problem is the complex exponential. The [complex logarithm](https://en.wikipedia.org/wiki/Complex_logarithm#Problems_with_inverting_the_complex_exponential_function) needs to be multi-valued, so multiple choices give distinct left inverses.