Two short questions:

• Is there any work classifying the lattice of subcategories of an arbitrary 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?