homomorphism
|ho-mo-morph-ism|
🇺🇸
/ˌhoʊməˈmɔːrfɪzəm/
🇬🇧
/ˌhɒməˈmɔːfɪzəm/
mapping that preserves form
Etymology
'homomorphism' originates from German, specifically the word 'Homomorphismus', where 'homo-' meant 'same' and 'morphē' (from Greek) meant 'form'.
'homomorphism' changed from the German mathematical term 'Homomorphismus' (itself built from Greek elements) and eventually became the modern English word 'homomorphism' in mathematical usage in the late 19th/early 20th century.
Initially, the components suggested 'same form' or 'same shape', but over time it evolved into its current technical meaning of 'a structure-preserving map between algebraic objects'.
Meanings by Part of Speech
Noun 1
a mapping between two algebraic structures of the same type that preserves the operations or relations defining those structures (e.g., f(xy)=f(x)f(y) for a group homomorphism).
A group homomorphism f: G → H preserves the group operation: f(xy) = f(x)f(y).
Synonyms
Noun 2
in a more general or categorical sense, a morphism between objects that respects the relevant structure or operations specified for that category.
In category theory, many familiar notions (groups, rings, vector spaces) have homomorphisms as the appropriate morphisms between objects.
Synonyms
Last updated: 2025/08/19 11:32