Tannaka Duality

A reconstruction correspondence that recovers a (pro-)algebraic group (or group scheme) from the tensor category of its finite-dimensional linear representations together with a choice of fibre functor to vector spaces; conversely, the category of representations is the primary invariant of the group.

A duality principle and reconstruction theorem that recovers an algebraic object (such as a proalgebraic group, group scheme, or Hopf algebra) from a suitably rigid tensor category of its linear representations together with a fiber functor to vector spaces.