If $(X;*)$ and $(X;\circ)$ are binary systems then $(X;*)\Longrightarrow (X;\circ)$ if $(x*y)\circ z = (x*z)*(y*z)$ where $(X;\circ)$ is the doubling algebra of the source algebra $(X;*)$. Obviously there are many mutual influences on the types of $(X;*)$ and $(X;\circ)$. In this paper we investigate several of these mutual influences, including when $(X;*)$ is a group, $B$-algebra, a cancellative semigroup with identity.