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