These are all references to a classroom number of the California Institute of the Arts (CalArts).
Mona's Academy of the Arts is on Avenue 113 in Paris, the number on the door of the brothel is A113, in the stable there's a numberplate inscribed with A113 - "ParArts, quality since 1870", a map reference is A1-13. " A113" appears a lot throughout the game."Dairy farmer" and "cow" refer to Insult Swordfighting from the Monkey Island series. During an argument in the game insults are hurled, such as: " SCUMMbag", "dairy farmer" and "cow".Mona introduces herself as "a mighty opera singer!" similar to Guybrush Threepwood declaring himself "a mighty pirate!".Mona mistakes a dead chicken for a rubber chicken with a pulley in the middle.