Is Ceres in the inner solar system or outer solar system?
Inner. The entire asteroid belt is in the Inner Solar System (now). The definition of "Inner" vs. "Outer" is non-arbitrary, based on the current "frost line", approx. 5 a.u. radius.

https://en.wikipedia.org/wiki/Frost_line_%28astrophysics%29

https://en.wikipedia.org/wiki/Solar_System#Inner_Solar_System