Category:Monoid Homomorphisms
Jump to navigation
Jump to search
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.
M
- Monoid Epimorphisms (empty)
- Monoid Isomorphisms (empty)
Pages in category "Monoid Homomorphisms"
This category contains only the following page.