In the tales the cat may be a guise in which the witch transforms herself. Or the cat may be the witch's alter ego. The cat will be the witches "fetch." Often in Fairy tales, the secret witch's identity is revealed through the fate of the cat. When the cat is killed, the witch simultaneously dies also. Or if the cat is harmed, often by an amputation of it's paw, a previously unsuspected witch suddenly and mysteriously sports identical injuries or scars.
This classic tale is an example that combines all the above motifs. It is called "The Tale of Kowashi's Mother". It is Japanese story of magical identity-theft.
Kowashi and his nice, normal mother live in a small village at the foot of a mountain. One day, all of a sudden, Kowashi notices that Mom's teeth are exceptionally long, sharp and pointy. And she has also suddenly developed a taste for fish heads and bones.
Their neighbor, a fisherman, comes home very late one night, carrying a basket of fish and is attacked by a pack of wild cats. The fisherman fights them off but the brazen cats refuse to retreat. One shouts, "Get Old Lady Kowashi!"
A huge raggedy gray cat appears. The fisherman whacks it on the head. As the sun comes up, the cats disappear. Kowashi wakes up to find Mom in the kitchen, her head all bandaged up, chewing on fish bones. He wonders....
Kowashi goes to school. When he returns home, his neighbor the fisherman is waiting for him and recounts his nocturnal adventure, including the part about, "Old Lady Kowashi!"
Kowashi enters his house where his mother,upon seeing him, arches her back and hisses. Kowashi decides that this cannot be his mother. A "witch-cat" must have killed her and stolen her image or so he believes. He slices off her head with a sword. At his feet lies a huge, ragged gray cat.
I hope you enjoyed the telling of this tale.
Brightest of Blessings,