Number & MeasureGreek → English
Homomorphism
/ˌhɒməˈmɔrfɪzəm/noun
A map between two algebraic structures that preserves the operations, without needing to be reversible.
The Greek roots
ὁμός
homós
same, shared
μορφή
morphḗ
form, shape
Literally: “same form”
The story of the word
Structure travels one way here. A homomorphism carries the operations of one object faithfully into another, but may collapse things on the way; add reversibility and it becomes an isomorphism. Crystallographers and chemists used homomorph first, for compounds of matching shape, before group theorists took the term over in the closing decades of the nineteenth century.
- How it travelled
- Ancient Greek → German → English
- First recorded
- 19th century
The same roots elsewhere
Other languages reached for exactly the same Greek pieces.
Same family
isomorphismautomorphismhomogeneoushomonym
In a sentence
The determinant is a homomorphism from matrices to numbers under multiplication.
Every homomorphism has a kernel, and the kernel tells you what got lost.