We present a method to construct explicitly L-infinity algebras governing
simultaneous deformations of various kinds of algebraic structures and of their
morphisms. It is an alternative to the heavy use of the operad machinery of the
existing approaches. Our method relies on Voronov's derived bracket
construction.Comment: 20 pages. Final version, accepted for publication, and significantly
shorter than version v1. Our previous submission arXiv:1202.2896v1 has been
divided into two parts. The present paper contains the algebraic applications
of the theory, while the geometric applications are the subject of the paper
arXiv:1202.2896v2 ("Simultaneous deformations and Poisson geometry"