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

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.