Category:Definitions/Monoid Homomorphisms
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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.
Subcategories
This category has the following 2 subcategories, out of 2 total.
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Pages in category "Definitions/Monoid Homomorphisms"
The following 6 pages are in this category, out of 6 total.