Morphism

Summary

A morphism is an arrow $f \colon A \to B$ of a category, from its domain $A$ to its codomain $B$. Morphisms abstract structure-preserving maps such as group homomorphisms, linear maps and continuous maps. Isomorphisms, endomorphisms and automorphisms are special morphisms defined only through domains, codomains and composition. Much of category theory consists of describing objects by the morphisms into them and out of them.