  The decoupling technique is a fundamental tool in quantum information theory
with applications ranging from quantum thermodynamics to quantum many body
physics to the study of black hole radiation. In this work we introduce the
notion of catalytic decoupling, that is, decoupling in the presence of an
uncorrelated ancilla system. This removes a restriction on the standard notion
of decoupling, which becomes important for structureless resources, and yields
a tight characterization in terms of the max-mutual information. Catalytic
decoupling naturally unifies various tasks like the erasure of correlations and
quantum state merging, and leads to a resource theory of decoupling.
