The deformation complex of an algebra over a colored PROP P is defined in
terms of a minimal (or, more generally, cofibrant) model of P. It is shown that
it carries the structure of an L_\infty-algebra which induces a graded Lie
bracket on cohomology.
As an example, the L_\infty-algebra structure on the deformation complex of
an associative algebra morphism g, with the underlying cochain complex
isomorphic to the Gerstenhaber-Schack complex of g, is constructed. Another
example is the deformation complex of a Lie algebra morphism. The last example
is the diagram describing two mutually inverse morphisms of vector spaces. Its
L_\infty-deformation complex has a nontrivial constant term.
Explicit formulas for the L_\infty-operations in the above examples are
given. A typical deformation complex of a diagram of algebras is a
fully-fledged L_\infty-algebra with nontrivial higher operations.