morphism UK /ˈmɔːfɪzəm/US /ˈmɔɹfɪzəm/ noun2 •(formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises. •Being or having distinct variants of a plant or animal species in the same locale; polymorphism. formsmorphisms