>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!