There are several factors to consider when determining if an Abyssinian cat is the right fit for your household. Some things to consider include:

1. Activity level: Abyssinian cats are known for their high energy and playful nature. If you have a active household and enjoy playing with your cat, an Abyssinian may be a good fit.
2. Grooming: Abyssinian cats have a short, fine coat that requires regular grooming to keep it in good condition. If you are willing to commit to regular grooming, an abyssinian may be a good fit.
3. Personality: Abyssinian cats are known for their intelligence and curious nature. They can be quite active and enjoy exploring their environment. They also have a tendency to be independent, and may not be as demanding of attention as other breeds. If you are looking for a cat that is independent, an abyssinian may be a good fit.
4. Living arrangement: Abyssinian cats are good for apartment living as long as they have enough space to run around and play.
5. Health: Abyssinian cats are generally healthy, but they can be prone to certain genetic health conditions, such as progressive retinal atrophy (PRA) and hip dysplasia.

Ultimately, the best way to determine if an abyssinian cat is the right fit for your household is to spend time with one and see how you and your family interact with the cat.