monic-and-epic
|mo-nic-and-ep-ic|
🇺🇸
/ˌmɑnɪk ænd ˈɛpɪk/
🇬🇧
/ˌmɒnɪk ænd ˈepɪk/
both monomorphism and epimorphism
Etymology
'monic-and-epic' originates from modern mathematical English, specifically as a compound of the terms 'monic' and 'epic' used in category theory; 'monic' ultimately comes from Greek 'monos' meaning 'single', and 'epic' is built from the Greek prefix 'epi-' ('upon') combined with 'morphe' ('form') as in 'epimorphism'.
'monic-and-epic' developed from the 20th-century coinages 'monomorphism' and 'epimorphism' (from Greek roots) which were shortened to 'monic' and 'epic' in informal mathematical usage; these shortened adjectives were then compounded to describe a morphism possessing both properties.
Initially the Greek roots related to 'single' and 'form/upon form', but in modern mathematical usage the terms came to denote specific categorical properties; 'monic-and-epic' now specifically denotes a morphism that is both a monomorphism and an epimorphism.
Meanings by Part of Speech
Noun 1
a morphism that is both monic and epic; i.e., a morphism that satisfies the definitions of both monomorphism and epimorphism.
The category contains a monic-and-epic that is not invertible.
Synonyms
Adjective 1
being both a monomorphism (monic) and an epimorphism (epic); used in category theory to describe a morphism that has both properties.
In many categories a monic-and-epic morphism need not be an isomorphism.
Synonyms
Last updated: 2025/10/13 15:03