A parameterization process, functorially
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 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.
Keywords
Cite
@article{arxiv.0908.4491,
title = {A parameterization process, functorially},
author = {César Dominguez and Dominique Duval},
journal= {arXiv preprint arXiv:0908.4491},
year = {2009}
}