bimorphism
|bi-mor-phis-m|
🇺🇸
/baɪˈmɔːr.fɪ.zəm/
🇬🇧
/baɪˈmɔː.fɪ.zəm/
both mono and epi
Etymology
'bimorphism' is formed from the prefix 'bi-' (from Latin 'bi-', meaning 'two' or 'twice') and 'morphism' (from Greek 'morphē', meaning 'form' or 'shape'), literally conveying 'two-form' or 'two-aspect form'.
'bimorphism' arose in mathematical usage by prefixing 'bi-' to the existing term 'morphism'. The term 'morphism' entered mathematical language in the 19th–20th centuries and was popularized in category theory (mid-20th century) by authors such as Eilenberg and Mac Lane; 'bimorphism' became used to denote a morphism that is both monomorphism and epimorphism.
Originally a compound meaning 'two-form' (from its parts), it became specialized in modern mathematics to mean specifically a morphism having both monic and epic properties; in concrete settings it is often interpreted as a bijection but in abstract category-theoretic contexts it does not necessarily imply an inverse.
Meanings by Part of Speech
Noun 1
in category theory, a morphism that is both a monomorphism and an epimorphism (i.e., has both monic and epic properties).
In many categories a bimorphism need not be an isomorphism.
Synonyms
Noun 2
in concrete categories (or informal contexts), a morphism whose underlying map is both injective and surjective (i.e., bijective as a set map), though this need not imply an inverse morphism.
When considered as functions between sets, certain bimorphisms are simply bijections.
Synonyms
Last updated: 2025/08/26 20:13