Category:Definitions/Homomorphisms (Abstract Algebra)

This category contains definitions related to homomorphisms in the context of abstract algebra.
Related results can be found in Category:Homomorphisms (Abstract Algebra).

Let $\struct {S, \circ}$ and $\struct {T, *}$ be algebraic structures.

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

Let $\circ$ have the morphism property under $\phi$, that is:

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

Then $\phi$ is a homomorphism.