Lack of exercise can lead to a number of health problems in Abyssinian cats. These include:

1. Obesity: Abyssinian cats are prone to weight gain and obesity if they do not get enough physical activity. This can lead to health problems such as arthritis, heart disease, liver disease, and other metabolic disorders.
2. Decreased muscle tone: Cats that do not exercise regularly can experience a decline in muscle tone, which can cause them to become stiff and experience pain, especially in their joints.
3. Decreased flexibility: Inactivity can cause a decrease in flexibility, which can limit the cat’s ability to move freely and can cause pain.
4. Decreased immune function: Regular physical activity has been shown to boost the immune system and help prevent disease. Cats that do not get enough exercise are more prone to illness and infection.
5. Behavioral problems: Cats that do not get enough physical activity may develop behavioral problems such as aggression, destructive behavior, and inappropriate elimination.
6. Dental problems: Lack of exercise can also lead to dental problems, as chewing is an important part of a cat’s natural physical activity. Chewing on toys and other objects can help keep the teeth and gums healthy and strong.
7. Decreased cardiovascular function: Exercise is important for maintaining cardiovascular health. Cats that do not get enough physical activity may experience a decline in cardiovascular function, which can lead to heart disease and other health problems.

In order to prevent these health problems, it is important to provide your Abyssinian cat with regular physical activity. This can include playtime, interactive toys, and puzzle feeders. You may also consider incorporating interactive toys into your cat’s daily routine, as well as providing a scratching post or climbing tree to encourage exercise and play. Regular visits to the vet can help monitor your cat’s health and detect any potential problems early.