English

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.

Keywords

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

R2 v1 2026-06-21T12:50:09.996Z