An operation in some class of universal algebras that associates with a given set of algebras from this class the "weakest free" (in a certain sense) algebra of the same class that contains subalgebras isomorphic to the given algebras and generating them. At present the terminology is close to that of a free product.
This terminology is not used in Western literature.
Free composition. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Free_composition&oldid=17608