Two short questions:

- Is there any work classifying the lattice of subcategories of an arbitrary (sufficiently small) category, similar to the way that the set of subsets of set $\mathcal{S}$ is isomorphic to the functions $\mathcal{S}\to\mathbf{2}$, where $\mathbf{2}$ is a two point set?

- Is there standard notation denoting the lattice of subcategories of some category?