Derived A(infinity)-algebras in an operadic context

Derived A1–algebras were developed recently by Sagave. Their advantage over classical A1–algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A1–algebras can be viewed as algebras over an operad. More specifically, we describe how this operad arises as a resolution of the operad dAs encoding bidgas, ie bicomplexes with an associative multiplication. This generalises the established result describing the operad A1 as a resolution of the operad As encoding associative algebras. We further show that Sagave’s definition of morphisms agrees with the infinitymorphisms of dA1–algebras arising from operadic machinery. We also study the operadic homology of derived A1–algebras.