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

TL;DR

This paper revisits Hugo Volger's 1967 work, providing a modern, constructive proof related to free algebras and analyzing its influence on later research.

Contribution

It offers a modern reinterpretation of Volger's proof, highlighting its constructive nature and its anticipation of subsequent developments in algebra theory.

Findings

Provides a modern account of Volger's proof

Shows the proof's constructive approach to free algebras

Analyzes the influence on later algebraic research

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.