Number & MeasureGreek → English
Monomorphism
/ˌmɒnoʊˈmɔːrfɪzəm/noun
A morphism that can be cancelled on the left, generalising the idea of a map that sends distinct things to distinct things.
The Greek roots
μόνος
mónos
single, alone
μορφή
morphḗ
form, shape
Literally: “single-forming”
The story of the word
The twin of epimorphism, and the pair replaced injective and surjective when category theory arrived in the 1940s. The mono says one: no two inputs are allowed to collapse onto a single output. Biology got there first with its own monomorphism, meaning a species whose members all look alike, which is the opposite of the dimorphism that makes a peacock and a peahen look unrelated.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 20th century
Same family
monopolymonolithmorphologyepimorphism
In a sentence
The inclusion of a subgroup is always a monomorphism.
Show that a monomorphism with a left inverse splits.