There's an easy way to settle if the category of \\(X\\)s is a \\(X\\) itself.

Take \\(X\\) to be sets. The question of whether \\(\mathbf{Set}\\), the category of sets, is itself is a set (a set of all sets) gives [Cantor's paradox](https://ncatlab.org/nlab/show/Cantor%27s+paradox).