  The parameterization process used in the symbolic computation systems Kenzo
and EAT is studied here as a general construction in a categorical framework.
This parameterization process starts from a given specification and builds a
parameterized specification by adding a parameter as a new variable to some
operations. Given a model of the parameterized specification, each
interpretation of the parameter, called an argument, provides a model of the
given specification. Moreover, under some relevant terminality assumption, this
correspondence between the arguments and the models of the given specification
is a bijection. It is proved in this paper that the parameterization process is
provided by a functor and the subsequent parameter passing process by a natural
transformation. Various categorical notions are used, mainly adjoint functors,
pushouts and lax colimits.
