Here’s one of the crosseffects.  It stands for a physical interaction, and is notated so that the arithmetic within the curly bracket is left to be determined.
	What arithmetic can be done within the curly brackets to convert this representation to a term that works as an abstract mathematical term?  We want that term to be an exact analogy to the physical interaction it stands for.  If it is an exact analogy, we don’t have to care whether it is “concrete” or “abstract” ……. We can use it in abstract math.