Captain "Mayonnaise" Quirke was the Captain of the Day Watch, before the two Watches were combined to form the City Watch. He was called 'Mayonnaise' because he is thick, rich and oily, and smells faintly of eggs - he doesn't have the imagination to be a bad man, but instead deals in the type of generalised unpleasantness that slightly tarnishes the soul of all who come into contact with it: rather like British Rail.
Believes that a shiny breastplate and a plume on his helmet make him important.
Even in a world where speciesism is more likely than racism, he is described as the sort of man who will always pronounce the word "negro" with an extra "g." He believes that all dwarfs and all trolls are automatically in the wrong because they aren't human. A typical bullying copper of the sort that makes small businesses pay him protection to make sure that they don't have any trouble, and who never pays for meals at city restaurants because otherwise he would make trouble for them.
Quirke: "I've got four years of good conduct, I have-"
Sam Vimes-as-John Keel: "No, that was four years Not Found Out!"
He later rises to prominence under Captain Findthee Swing and continues his role in the Day Watch over the years.
He is described as having the gnawing, nerve-sapping vitriol of the mediocre: not bright enough to get anywhere on merit he can only hate what he can't achieve and rubbish it. And he never thinks for himself; he does what he is told, as thinking is too difficult for him.
Then-Corporal Carrot lays him out with a sweet uppercut in Men at Arms and then establishes with the Patrician that the two Watches should be conjoined into one police force, under the command of Vimes. Quirke is never heard of again, so presumably Vimes turfs him out of the Watch, (for a second time - or rather the first time, from Vimes point of view, owing to Time travel being involved the first time round.)