Maybe someone can explain better, but I don't think it's a coincidence.. In category theory, there is a general notion of "exponential object". This works like

Maybe someone can explain better, but I don't think it's a coincidence.. In category theory, there is a general notion of "exponential object". This works like normal exponentiation in various categories of numbers, and like modus ponens (and also reversed - given exponent and power, you can deduce the base) in various categories of logic.