For $H$ a Hopf algebra, with bijective antipode. For a right, and a left, $H$-comodule $(V,\alpha_R)$, and $(W,\alpha_L)$ respectively, the **cotensor product** of $V$ and $W$ is
$$
V \square_H W := \ker(\alpha_R \otimes \text{id} - \text{id} \otimes \alpha_L:V \otimes W \to V \otimes H \otimes W).
$$

When does it hold that $$ V \square_H H ~~~ \simeq V? $$