Constant Quantities And Constant Domains

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 is a number that varies with the time (say, if 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 where is our notion of time and our notion of number.

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