A Universal Algebraic Survey of C∞-Rings

Abstract

This survey brings a detailed and systematic exposition of some fundamental results regarding the
Universal Algebra of C∞−rings. Some of these were nowhere to be found – stated or proved – in
the current literature. Our main contribution is to bundle these results up in a single text, using
the unifying language of Universal Algebra and referring the reader to detailed proofs. Such a
presentation is inspired by the treatment given by D. Joyce in [1] to some concepts involving these
rings. Thus, we provide a comprehensive material with many known “taken for granted” results and
constructions used everywhere in the literature about C∞−rings and their applications, providing a
“propaedeutic exposition” for the reader’s benefit.