English

A parameterization process, functorially

Logic in Computer Science 2009-09-01 v1 Category Theory

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}
}
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