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[latex]null[/latex][latex]\lettrine[lhang=0.17]{A}{category} is an embarrassingly simple concept. A category consists of \newterm{objects} and \newterm{arrows} that go between them. That's why categories are so easy to represent pictorially. An object can be drawn as a circle or a point, and an arrow\ldots{} is an arrow. (Just for variety, I will occasionally draw objects as piggies and arrows as fireworks.) But the essence of a category is \emph{composition}. Or, if you prefer, the essence of composition is a category. Arrows compose, so if you have an arrow from object $A$ to object $B$, and another arrow from object $B$ to object $C$, then there must be an arrow --- their composition --- that goes from $A$ to $C$.[/latex]