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.

Preface In my previous blog post I used, without proof, the fact that the initial algebra of the functor $latex I + h \otimes -$ is a free monoid. The proof of this statement is not at all trivial …

Mathematicians tend to study classes of invertible processes: groups, rings, groupoids. Informaticists tend to study classes of general processes: monoids, semirings, categories.

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