Category:Definitions/Morphism Property

This category contains definitions related to Morphism Property.
Related results can be found in Category:Morphism Property.

Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be a mapping from one algebraic structure $\struct {S, \circ}$ to another $\struct {T, *}$.

Then $\circ$ has the morphism property under $\phi$ if and only if:

$\forall x, y \in S: \map \phi {x \circ y} = \map \phi x * \map \phi y$