Gerstenhaber-Schack diagram cohomology from operadic point of view

TL;DR

This paper demonstrates that Gerstenhaber-Schack diagram cohomology can be understood as operadic cohomology by relating it to Ext in the category of operadic modules, providing a new conceptual framework.

Contribution

It establishes a novel operadic perspective on Gerstenhaber-Schack cohomology, connecting it to the broader theory of operadic cohomology for algebraic structures.

Findings

Gerstenhaber-Schack cohomology is operadic cohomology.

Operadic cohomology can be computed as Ext in the category of operadic modules.

Provides a new method to analyze diagram cohomology using operadic techniques.

Abstract

We show that the operadic cohomology for any type of algebras over a non-symmetric operad A can be computed as Ext in the category of operadic A-modules. We use this principle to prove that the Gerstenhaber-Schack diagram cohomology is operadic cohomology.