Deformations of Algebras with 2-Extensions

TL;DR

This paper explores how 2-extensions of algebras influence their deformation theory, offering multiple perspectives and correcting an existing error in the literature.

Contribution

It introduces a (2, 0)-category framework for algebra deformations and clarifies previous misunderstandings in the field.

Findings

Established connections between 2-extensions and algebra deformations

Provided three different viewpoints on deformation theory

Corrected a known error in existing literature

Abstract

We apply the notion of 2-extensions of algebras to the deformation theory of algebras. After standard results on butterflies between 2-extensions, we use this (2, 0)-category to give three perspectives on the deformation theory of algebras. We conclude by fixing an error in the literature.