We will describe a class of inclusions of C*-algebras that admits a notion of a standard invariant akin to that of subfactors. We consider unital inclusions of C*-algebras with a conditional expectation, and characterize the abstract property of C*-discreteness precisely in terms of inclusions obtained from a generalized crossed product construction. These crossed products arise from what we call a C*-quantum dynamics and a generalized Q-system, which are given formally by an action of a unitary tensor category on a C*-algebra and a C*-algebra object in that category. Our formalism includes many infinite-index inclusions, and during the talk, we will review synthetic and natural examples of C*-discrete inclusions. As an application, we will describe a generalized Galois correspondence for C*-algebras, describing a certain lattice of intermediate C*-subalgebras to a given C*-discrete inclusion in terms of a lattice of C*-algebra objects. Finally we show that C*-discrete extensions of simple C*-algebras by a free and outer quantum dynamics remain simple. This is joint work with Brent Nelson.