>Let's call this category \\(\mathcal{D}\\). A functor \\(F: \mathcal{C} \to \mathbf{Set} \\) is a database consisting of a set of Germans.

Is this correct? Shouldn't it be "A functor \\(F: \mathcal{D} \to \mathbf{Set} \\) is a database consisting of a set of Germans"?