A parameterization process as a categorical construction
Abstract
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 transforming some operations into parameterized operations, which depend on one additional variable called the parameter. 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 free functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits.
Cite
@article{arxiv.0908.3634,
title = {A parameterization process as a categorical construction},
author = {Dominique Duval and César Dominguez},
journal= {arXiv preprint arXiv:0908.3634},
year = {2009}
}