Category:Monoid Homomorphisms

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This category contains results about Monoid Homomorphisms.
Definitions specific to this category can be found in Definitions/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.

Subcategories

This category has the following 2 subcategories, out of 2 total.

Pages in category "Monoid Homomorphisms"

This category contains only the following page.