monomorphism
|mo-no-mor-phism|
🇺🇸
/ˌmɑːnoʊˈmɔːrfɪzəm/
🇬🇧
/ˌmɒnəˈmɔːfɪz(ə)m/
single, injective map
Etymology
'monomorphism' originates from Greek elements 'mono-' and 'morphē', where 'mono-' meant 'single' and 'morphē' meant 'form' or 'shape'.
'morphism' was coined in mathematical usage in the 20th century from Greek 'morphē' (form) with the suffix '-ism'; combining it with the prefix 'mono-' produced 'monomorphism' to denote a 'single-form' mapping with a specific categorical property.
Initially formed from roots meaning 'single form', the term evolved into the technical mathematical meaning 'an injective (left-cancellative) morphism in category theory or an injective homomorphism in algebra.'
Meanings by Part of Speech
Noun 1
in category theory, a morphism f: A → B that is left-cancellative: for any two morphisms g,h: X → A, f ∘ g = f ∘ h implies g = h. Often thought of as the categorical analogue of an injective map.
In many categories, every monomorphism is an injective function on underlying sets, but the categorical notion is more general.
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Noun 2
in algebra (groups, rings, modules), a homomorphism that is injective; i.e., a homomorphism whose kernel is trivial.
The inclusion map from a subgroup into its parent group is a monomorphism of groups.
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Last updated: 2025/08/26 20:29