Definition:Morphism Property
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Definition
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:
- $\forall x, y \in S: \map \phi {x \circ y} = \map \phi x * \map \phi y$
Also known as
Some sources call this property the homomorphism condition.
Sources
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.10$