Homotopy Transfer Theorem for Linearly Compatible Di-algebras

Abstract

This paper studies the operad of linearly compatible di-algebras, denoted by $A{s}^2$, which is a nonsymmetric operad encoding the algebras with two binary operations that satisfy individual and sum associativity conditions. We also prove that the operad $A{s}^2$ is exactly the Koszul dual operad of the operad ${}^{2}As$ encoding totally compatible di-algebras. We show that the operads $A{s}^2$ and ${}^{2}As$ are Koszul by rewriting method. We make explicit the Homotopy Transfer Theorem for $A{s}^2$-algebras.

References in corpus (1)

• Operads of compatible structures and weighted partitions