Cats have evolved in a solitary lifestyle but domestication has forced them into social groups with either people or cats and dogs. This is something they are often unable to cope with.
Manifestations of this difficulty may show up as inappropriate urination within the home, licking bald patches in their coat, hiding, aggression, inappetence, etc.
Be aware that introducing new dogs, cats and people into your cat's life may be a problem for it. Your veterinarian or breeder may be able to suggest techniques to make the transition as smooth as possible, ie. tranquillisation of one or both parties; separation by a door for a few days; caged introduction of one or both. Sometimes a cat is so territorial that it will never suffer another feline in its world.
Cats are frequently bitten by other dominant cats who feel their territory has been invaded. It is usually a night time activity. If this occurs, trying to keep the cat indoors of an evening often helps. Having a dog in the backyard keeps the other cat out.
Bear in mind that the Feline Immunodeficiency Virus (FIV - the cause of feline AIDs) is transmitted by biting, so preventing fights is important to stop the transmission of disease to your loved one.