I originally posted this on Maths SE, but then I thought it MO might be more fitting.

Let $k$ be a characteristic $0$ field and let $G$ be a linear algebraic group scheme over $k$. Then is it true that $G$ is reductive if and only if the category of representations of $G$, $\mathsf{Rep}(G)$ is semi-simple ?

P/s: $\mathsf{Rep}(\mathcal{G})$ is defined as the functor category $[\mathcal{G}, \mathcal{C}]$, where $\mathcal{G}$ is a groupoid and $\mathcal{C}$ is some category.