  Starting from a biased definition of a properad, we describe explicitly
algebras over the cobar construction of a properad. Equivalent description in
terms of solutions of generalized master equations, which can be interpreted as
homological differential operators, are explained from the properadic point of
view. This is parallel to the Barannikov's theory for modular operads. In
addition to well known IBL-homotopy algebras, the examples include their
associative analogues, which we call $IBA$-homotopy algebras, and a combination
of the above two.
