Parameterized differential Galois theory

Classical Galois theory studies symmetry groups of solutions of algebraic equations. Differential Galois theory studies symmetry groups of solutions of linear differential equations. We discuss a so-called parameterized differential Galois theory which studies symmetry groups of solutions of linear differential equations with parameters. The groups that arise are linear differential groups given by differential equations (not necessarily linear) on functions in parameters. We also discuss in this connection derivations on abelian categories and differential Tannakian categories.