On the perturbation lemma, and deformations

TL;DR

This paper revisits the homological perturbation lemma, exploring its implications and connections to deformation theory, revealing new insights and consequences in the context of algebraic structures.

Contribution

It provides a new perspective on the perturbation lemma and highlights its relevance to deformation theory, including some non-standard consequences.

Findings

Identification of non-standard consequences of the perturbation lemma

Relevance of the lemma to deformation theory

New insights into homological algebra

Abstract

We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.