Galois connection
As suggested by the notation, the residuals are a form of quotient. More precisely, for a given "x" in "L", the unary operations "x"• and "x"\ are respectively the lower and upper adjoints of a Galois connection on L, and dually for the two functions •"y" and /"y". By the same reasoning that applies to any Galois connection, we have yet another definition of the residuals, namely,