English

Revisiting Hugo Volger's paper Uber die Existenz der freien Algebren

Category Theory 2026-04-07 v2

Abstract

We give a modern account of Hugo Volger's 1967 paper which, motivated by the construction of free algebras for a Lawvere-Linton theory, gives a very constructive proof that the left Kan extension of a product-preserving Set-valued functor is product-preserving. We also analyze how it anticipates, and in part even exceeds, subsequent work of the 1970s.

Keywords

Cite

@article{arxiv.2412.20286,
  title  = {Revisiting Hugo Volger's paper Uber die Existenz der freien Algebren},
  author = {Matias Menni and Walter Tholen},
  journal= {arXiv preprint arXiv:2412.20286},
  year   = {2026}
}

Comments

This version breaks down the proof of a key Lemma in Volger's paper into easy-to-follow steps