  If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its
bracket can be written in a form that mimics a "double sided semidirect
product". It is called the {\it knit product} of the two subalgebras then. The
integrated version of this is called a {\it knit product} of groups --- it
coincides with the {\it Zappa-Sz\'ep product}. The behavior of homomorphisms
with respect to knit products is investigated.
