We present an {\em axiomatic} characterization of  models {\em fully-complete}
for {\em ML-polymorphic types} of system F. This axiomatization is given
for {\em hyperdoctrine} models, which arise as {\em adjoint models}, i.e.
{\em co-Kleisli categories} of suitable {\em linear categories}. 
Examples of adjoint models can be obtained from categories of {\em Partial 
Equivalence Relations} over {\em Linear Combinatory Algebras}.
We show that a special linear combinatory algebra of {\em partial involutions}
induces an hyperdoctrine which satisfies our axiomatization, and hence it 
provides a fully-complete model for ML-types.