Category:Homomorphisms

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This category contains results about Homomorphisms in the context of Abstract Algebra.
Definitions specific to this category can be found in Definitions/Homomorphisms.


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

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.

Subcategories

This category has the following 11 subcategories, out of 11 total.

A

E

F

G

I

M

Q

R

S