First, category theory is not about graphs. Categories are not graphs. There not even graphs with a tiny bit of structure on top. Categories are abstractions of mathematicals structures, which can be represented as graph. One can even argue that applications of category theory are simply about structuring the underlying objects and relations in such a way that what we want to prove is shown by a basic diagram. An intuition for this is that you can do category theory without using the graphs.
I don’t really get this objection. I think you might have too dismal a view of graphs? Category theoretic notions use a bunch of diagrams and only talks about their diagrammatic properties—since the representation as graphs is the prominent representation in field, and is what people think in, then what’s wrong with just talking about graphs?
As a side note, I remember when I first encountered graphs as a kid, and thought they were the coolest thing in the world, due to being able to represent so much (and I hadn’t even seen Pearl yet!). Clearly she would’ve found category-theory-as-graphs-of-mathematical-objects a natural thing to do with graphs (with the only problem of not knowing any abstract math for the examples to make sense). I suspect others would, too.
I don’t really get this objection. I think you might have too dismal a view of graphs? Category theoretic notions use a bunch of diagrams and only talks about their diagrammatic properties—since the representation as graphs is the prominent representation in field, and is what people think in, then what’s wrong with just talking about graphs?
As a side note, I remember when I first encountered graphs as a kid, and thought they were the coolest thing in the world, due to being able to represent so much (and I hadn’t even seen Pearl yet!). Clearly she would’ve found category-theory-as-graphs-of-mathematical-objects a natural thing to do with graphs (with the only problem of not knowing any abstract math for the examples to make sense). I suspect others would, too.