cohomology

1 9.9

A part of math that uses algebra to study shapes and spaces

noun
/koʊhəˈmɑlədʒi/

Specialized

: cohomología

Now, there is no way I can possibly explain in simple terms what a cohomology class is.

Examples

It was understood that in order to construct unitary representations of a group of currents, one needs to use nontrivial cohomology of the group of coefficients with values in irreducible unitary representations of this group.

Academic text (2018)
Cohomology is a vital concept in algebraic topology that helps in understanding the shape and structure of cohomology spaces.
In many areas of mathematics, cohomology provides tools to classify and relate different topological properties.
The study of cohomology relies on various algebraic techniques to analyze the characteristics of complex spaces.

Surface Forms

cohomology singular

cohomologies plural

Morphology

cohomology = homology (semi-transparent) = co + homology

Formally built from the productive mathematical prefix 'co-' plus 'homology', but the precise meaning ('the dual theory') is specialized and not obvious to general learners.

Etymology

Cohomology starts with co- meaning 'together', like in cooperate, and ends with homology, whose root means 'same', like homonym or homogeneous. So, cohomology is a 'together' study of the 'same' features of a space and helps mathematicians find hidden structure in shapes and spaces.