  Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced by
Tao Zhang and Juan Li . We extend their theory to develop formal one-parameter
deformation theory of Lie-Yamaguti algebras. It turns out that the right
deformation cohomology which controls deformations in this context, is a
variant of Lie-Yamaguti algebra cohomology which we introduce in this paper. At
the end, we introduce the free object in the category of Lie-Yamaguti algebras
and prove that it is rigid.
