▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Operation
▾ N-operation
▾ Binary operation
▾ Enclosed binary operation
▾ Groupoid
▾ Groupoid homomorphism
Semigroup homomorphism
Formulation 0
Let $G$ and $H$ each be a D264: Semigroup.
A D18: Map $f : G \to H$ is a semigroup homomorphism from $G$ to $H$ if and only if \begin{equation} \forall \, x, y \in G : f(x y) = f(x) f(y) \end{equation}
Child definitions
» D1651: Monoid homomorphism