Category:Definitions/Antihomomorphisms

This category contains definitions related to Antihomomorphisms.
Related results can be found in Category:Antihomomorphisms.

Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be a mapping from one algebraic structure $\struct {S, \circ}$ to another $\struct {T, *}$.

Then $\phi$ is an antihomomorphism if and only if:

$\forall x, y \in S: \map \phi {x \circ y} = \map \phi y * \map \phi x$

For structures with more than one operation, $\phi$ may be antihomomorphic for a subset of those operations.