Derived A-infinty algebras in an operadic context

Derived A-infinity algebras were developed recently by Sagave. Their advantage over classical A-infinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A-infinity 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 A-infinity as a resolution of the operad As encoding associative algebras. We further show that Sagave’s definition of morphisms agrees with the infinity- morphisms of dA-infinity –algebras arising from operadic machinery. We also study the operadic homology of derived A-infinity algebras.