Definition:Morphism Property

Definition
Let $\phi: \left({S, \circ}\right) \to \left({T, *}\right)$ be a mapping from one algebraic structure $\left({S, \circ}\right)$ to another $\left({T, *}\right)$.

Then $\circ$ has the morphism property under $\phi$ iff:


 * $\forall x, y \in S: \phi \left({x \circ y}\right) = \phi \left({x}\right) * \phi \left({y}\right)$

Also known as
Some sources call this property the homomorphism condition.