Number & MeasureGreek → English
Cohomology
/ˌkoʊhəˈmɑlədʒi/noun
The algebraic theory dual to homology, assigning groups to a space by working with functions on its cells rather than the cells themselves.
The Greek roots
ὁμός
homós
same
λόγος
lógos
ratio, proportion
Literally: “the paired form of same-ratio”
The story of the word
A Latin prefix bolted onto a Greek compound, which purists dislike and everyone uses. Hassler Whitney is usually credited with fixing the term in 1938, when the dual theory turned out to carry a multiplication that homology lacks. That extra structure is the reason cohomology is the version most working topologists reach for first.
- How it travelled
- Ancient Greek → scientific coinage → English
- First recorded
- 20th century
The same roots elsewhere
Other languages reached for exactly the same Greek pieces.
Same family
homologyhomomorphismhomogeneoustopology
In a sentence
The cup product turns cohomology into a ring, which homology never manages.