Cats in the Matrix are controlled by a program. During the Sixth Matrix there were a number of cats, notably the black cat noticed by Neo during the Hotel Ambush, the black cat who woke Sati after the reload, Ash's cat Dinah, and Yoko's cat Yuki.
Programs[]
Dinah throwing Ash's hat to him, after he forgot to take it with him.
It is unclear whether a single program controls all cats, or each one is a separate Artificial Intelligence. In some cases, such as Ash's cat Dinah, they seem to exceed cats' normal intelligence.
Real World[]
Yuki wandering off towards the haunted house.
Cats presumably existed in the Real World before the Machine War and Operation Dark Storm led to the extinction of most animal and plant life, as the Matrix was designed to mirror the late 20th century.