  For a simplicial complex K on m vertices and simplicial complexes K1,...,Km a
composed simplicial complex K(K1,...,Km) is introduced. This construction
generalizes an iterated simplicial wedge construction studied by A. Bahri, M.
Bendersky, F. R. Cohen and S. Gitler and allows to describe the combinatorics
of generalized joins of polytopes P(P1,...,Pm) defined by G. Agnarsson. The
composition defines a structure of an operad on a set of finite simplicial
complexes. We prove the following: (1) a composed complex K(K1,...,Km) is a
simplicial sphere iff K is a simplicial sphere and Ki are the boundaries of
simplices; (2) a class of spherical nerve-complexes is closed under the
operation of composition (3) finally, we express multigraded Betti numbers of
K(K1,...,Km) in terms of multigraded Betti numbers of K, K1,...,Km using a
composition of generating functions.
