04.2 Morphisms and Mappings
4.2 Morphisms and Mappings A morphism is a map that preserves structure. It is the correct notion of transformation for a given mathematical setting. A plain function sends elements of one set to elements of another set. $$ f : X \to Y $$ A morphism does more. It respects the operations, relations, or laws that define the structures on $X$ and $Y$. For groups, the morphisms are group homomorphisms....