Cate can claim Amy as a dependent.
Step-by-step explanation:
The custodial parents can claim their child as the dependent, as a qualifying child for head of household filing status, for EIC, for the child tax credit and so on. But in case the parents get divorced, then the parent with whom the child spends the most time gets to claim the child as dependent.
In the above case, since Amy stays with Cate, Cate gets to claim Amy as dependent because she is staying with Cate only and spends the most time with her.