A cat and a mouse can live together, but this depends on a number of factors, including the cat's temperament, its training, and its previous experience with mice. Here are some points to think about on the subject:

1. The character of the cat:
Friendly or aggressive: there are cats that are characterized as loving and non-aggressive, and there are cats with strong hunting instincts. A friendly cat may be able to live with a mouse without chasing or harming it.
2. Education and socialization:
Cats that have been trained to be tolerant or have been exposed to mice since they were young may develop positive associations with mice. Proper socialization can help the cat understand that a mouse is not an enemy.

3. Age and experience:
Younger cats may be more inclined to chase mice, while some older cats may lose their lateral instincts. An older cat may be calmer and live peacefully with a mouse.
4. Types of mice:
There are different types of mice, some are more relaxed and some are more active. Calm mice may get along better with cats, while active mice may stimulate the cat's instincts.
5. Calculated environment:
If you want to try to live together, it is important to create a safe environment, where the mouse can feel protected. This can include hiding places, such as burrows or boxes, where the mouse can hide if the cat approaches.

6. Inserting a new mouse:
If you plan to introduce a mouse into a house where a cat already lives, it should be done gradually. You should take the cat out of the room where the mouse is at first, and then introduce the two gradually.
Summary:
A cat and a mouse can live together under certain conditions, but it depends on the character of each of them, training and socialization. If you want to try to live together, it is necessary to monitor and maintain positive relationships to avoid situations of tension or aggression.