When explaining category theory to my friends (which happens more than you might think), I often find myself summing the theory up as “the abstract study of variable quantities”. We analyse the notion of a variable quantity into two components: what the quantity *is*, and with what the quantity *varies*. To say that a quantity \(q\) *is* a number that *varies* with the time (say, if \(q\) is the position of a beetle as it walks along the edge of a ruler, or the angle in degrees that the sun makes with the horizon), we write \(q : T \to N\) where \(T\) is our notion of time and \(N\) our notion of number.