  Given a representation of a C*-algebra, thought of as an abstract collection
of physical observables, together with a unit vector, one obtains a state on
the algebra via restriction. We show that the Gelfand-Naimark-Segal (GNS)
construction furnishes a left adjoint of this restriction. To properly
formulate this adjoint, it must be viewed as a weak natural transformation, a
1-morphism in a suitable 2-category, rather than as a functor between
categories. Weak naturality encodes the functoriality and the universal
property of adjunctions encodes the characterizing features of the GNS
construction. Mathematical definitions and results are accompanied by physical
interpretations.
