>Sure, the objects are important, because that's where our data ends up by way of the functor. But with respect to **Puzzle 109**, we can factor every morphism into a string of ground arrows from the schema, so the kinds of queries you can perform can be reduced to questions about the schema.

I'd argue that the objects, (\\(X \in \mathcal{C}\\)), aren't that important since they can be represented by identity morphisms \\(id_X\\).

So basically, \\(F\\) is 'like' a function, but instead of mapping between sets, as a function does, a functor maps between morphism, including the trivial idenities.

In this sense, all that matters is where morphisms end up, and where the objects end up comes out for free!