Is it permissible to castrate a cat to keep it in the house, despite the danger of the procedure and the mother's desire to send it away, due to its frequent urination and foul odor?

Cat urine and feces are impure according to the majority of scholars, and whatever they touch must be purified. There is no objection to neutering a cat if it results in a recognized legitimate benefit or averts harm. An example of such a benefit is the need for the cat to drive away mice. If there is no such need, then it is preferable to keep the cat away from the house.