Number & MeasureGreek → English
Epimorphism
/ˌɛpɪˈmɔːrfɪzəm/noun
A morphism that can be cancelled on the right, generalising the idea of a map onto its whole target.
The Greek roots
ἐπί
epí
upon, onto
μορφή
morphḗ
form, shape
Literally: “forming onto”
The story of the word
Eilenberg and Mac Lane founded category theory in 1945 and needed names for the two halves of the old injective and surjective pair. ἐπί was chosen to echo the English word onto. The echo is imperfect and the imperfection is the interesting part: in the category of rings the inclusion of the integers into the rationals is an epimorphism without being onto anything much at all.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 20th century
Same family
epidemicepicentremorphologymonomorphism
In a sentence
In the category of sets, epimorphism and surjection coincide.
He asked whether the map was an epimorphism, not merely surjective on elements.