Category:Homomorphisms (Abstract Algebra)

From ProofWiki
Jump to navigation Jump to search

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

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

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.


This category has the following 20 subcategories, out of 20 total.