Sigmund is a Red Persian neutered male cat with copper-coloured eyes. He's famous among cats for his activity as psychotherapist, having learned techniques from his master including hypnosis sessions that he performs with his long fluffy tail. He lives into a large luxury villa over an hill.
Sigmund seems to be fairly well known among cats. It's known that Sancta had sessions with him, manifesting (according Francis's opinion) her distress for an alleged feeling of indifference from Francis.
Trivia: His name is a clear reference to Sigmund Freud, probably given to him by Sigmund (cat) 's human master because the man was himself a psychotherapist
Francis visits Sigmund after Sancta's suggestion, to understand what was happening and if he was actually going to turn insane (however have to be stressed how Francis was quite certain of his mental sanity and he's not especially confident in being help with a psychotherapy session).
Sigmund initially proves to be interested, sympathetic and eager to help, starting an hypnosis session but taking advantage of the temporary control over Francis's will, the Persian attempt unexpectedly to murder the detective forcing him to jump from the cliff of the villa's hill.
Pi appears and quickly get rid of Sigmund knocking him down the cliff and killing him.
Following the revelations at the end of the novel, it's clear how Sigmund was one of the non-Chronos's cats and non-black cats members of the Brotherhood of Black (or was possibly even controlled by them) and was attempting to stop the interference that a smart and famous cat as Francis could have caused.
After the ending of the novel, the death of Sigmund is a never-happened event and the cat is not going to remember about the Brotherhood of Black and the attempting murdering of Francis and is likely to going on with a quiet life of psychotherapist cat.