Varieties defined by natural transformations
Category Theory
2009-04-13 v1
Abstract
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.
Cite
@article{arxiv.0904.1678,
title = {Varieties defined by natural transformations},
author = {Jan Pavlík},
journal= {arXiv preprint arXiv:0904.1678},
year = {2009}
}
Comments
16 pages, submitted to Archivum Mathematicum, Masaryk University, Brno, Czech Republic