TT52: Tomb of Nakht, Sheikh Abd el-Qurna, Theban Necropolis - Cat enjoying fish underneath chairs of Nakht and Tawi.
Archaeologic evidence of cats in context with humans is first known about 4000 BC. This occurs with the start of organized agriculture, and maybe with the rodents that seem to find an interest in stored grains. It's very hard to tell the difference between a wild cat and a domestic one, but people typically lived on the fringe of agricultural land and would have been interesting to both desert cats from one side and swamp/floodplain cats from the other. Early in the 20th century, cats were not pets in Sudan: they wandered freely, entered people's homes at night to take care of vermin, but wouldn't stand to be touched. It is suspected that this type of behavior was the start of their domestication. Cats started as privileged luxury pets, but by 1500 BC, they were widespread in Egypt, appearing in comic artwork usually associated with mice.
While closely tied to religious deities, cats eventually superseded being representatives or go-betweens and were thought of as gods themselves. In their ability to protect a home from scorpions, snakes, and rodents, they were seen as divine protection from evil and misfortune.
Cats found their way to Crete by 900 BC, Greece by 500 BC, India by 300 BC, and China by 200 BC.
There's some speculation that as the empire faded, belief in the human aspects of the gods decreased, but animal beliefs became more intense. There are numerous large cat cemeteries in Egypt where they were buried by the thousands. The penalty for killing a cat (intentional or accidental) was death.
Baldwin, J. (1975). Notes and Speculations on the Domestication of the Cat in Egypt. Anthropos, 70(3/4), 428-448.
Flower, Stanley S. (1932) Notes on the Recent Mammals of Egypt, with a list of the Species Recorded from that Kingdom. Proceedings of the Zoological Society of London 101:369-450
""And whoever intentionally kills one of these animals is put to death, unless it be a cat or an ibis that he kills; but if he kills one of these, whether intentionally or unintentionally, he is certainly put to death, for the common people gather in crowds and deal with the perpetrator most cruelly, sometimes doing this without waiting for a trial. ... So deeply implanted also in the hearts of the common people is their superstitious regard for these animals and so unalterable are the emotions cherished by every man regarding the honour due to them that once, at the time when Ptolemy their king had not as yet been given by the Romans the appellation of "friend" <amici et socii populi Romani> and the people were exercising all zeal in courting the favour of the embassy from Italy which was then visiting Egypt and, in their fear, were intent upon giving no cause for complaint or war, when one of the Romans killed a cat and the multitude rushed in a crowd to his house, neither the officials sent by the king to beg the man off nor the fear of Rome which all the people felt were enough to save the man from punishment, even though his act had been an accident. And this incident we relate, not from hearsay, but we saw it with our own eyes on the occasion of the visit we made to Egypt."
--- Diodorus Siculus, The Library of History, Book I, 83
Diodorus is talking about Ptolemy XII, Cleopatra VII's father. At the time Diodorus was in Alexandria, Ptolemy was in Rome bribing Caesar and Pompey with borrowed money ... to put him back on the throne after being exiled. Cleopatra was 10 years old: it's not clear if she accompanied her father to Rome or not.>
I have heard three rumors about cats, but couldn't turn up references. If anyone can give me a solid reference, I will update it here.
1) As a sign of reverence, household cats did not have names (they were still cuddled & taken care of).
2) Phoenicians stole cats from Egypt and spread them across the Mediterranean (much like the stealing of silk worms from China).
3) Phoenicians routinely had ship cats.