Category:Definitions/Monoid Homomorphisms

This category contains definitions related to Monoid Homomorphisms.
Related results can be found in Category:Monoid Homomorphisms.

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

Let $\phi: S \to T$ be a mapping such that $\circ$ has the morphism property under $\phi$.

That is, $\forall a, b \in S$:

$\map \phi {a \circ b} = \map \phi a * \map \phi b$

Suppose further that $\phi$ preserves identities, that is:

$\map \phi {e_S} = e_T$

Then $\phi: \struct {S, \circ} \to \struct {T, *}$ is a monoid homomorphism.