Number & MeasureGreek → English
Morphism
/ˈmɔːrfɪzəm/noun
A structure-preserving map between two mathematical objects of the same kind.
The Greek roots
μορφή
morphḗ
form, shape
Literally: “a forming”
Follow a root:μορφή20 words
The story of the word
Homomorphism came first in nineteenth-century algebra, and morphism is what remains once category theory drops the qualifiers and treats the arrows as primitive. In a category the objects can be almost anything; what carries the mathematics is the arrows between them and the rule for composing two. The same μορφή shapes morphine, named after Morpheus who moulds the figures in dreams, and morphology, a word Goethe coined in the 1790s for the study of organic form.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 20th century
Same family
morphologyamorphousmetamorphosismorphine
In a sentence
A category is objects, morphisms between them, and a way of composing morphisms.
The identity morphism does nothing, which is precisely why it has to exist.