I was thumbing through a new book on causal inference, The Effect by Nick Huntington-Klein, and the following diagram caught my eye.

Then it made my head hurt. It looks like a category theory diagram. What’s that doing in a book on causal inference? And if it is a category theory diagram, something’s wrong. Either there’s a typo or the arrows are backward.

The diagram above is a valid commutative diagram, but for a coproduct rather than a product. That is, *X* × *Z* should be labeled *X* ⨿ *Z*. (For more on that, see my post on categorical products, and reverse all the arrows in your mind.)

But there’s no category theory going on here. This is an **influence diagram**. It says that *X* and *Z* influence *Y* directly (indicated by the diagonal arrows), but they also determine the product *X* × *Z* (the ordinary product of two numbers, no fancy category stuff) and this product in turn also influences *Y*.

After several unsuccessful attempts to get anywhere with Category Theory, I came across the introductory book by Harold Simmons, which I recommend very highly. He keeps the pace quite modest and the chapters short. This is certainly the friendliest introduction I have found.