Editing Algebraic topology (section)

===Cohomology===
{{Main|Cohomology}}
In [[homology theory]] and algebraic topology, '''cohomology''' is a general term for a [[sequence]] of [[abelian group]]s defined from a [[chain complex|cochain complex]]. That is, cohomology is defined as the abstract study of '''cochains''', [[chain complex|cocycle]]s, and [[coboundary|coboundaries]]. Cohomology can be viewed as a method of assigning [[algebraic invariant]]s to a topological space that has a more refined [[algebraic structure]] than does [[homology (mathematics)|homology]]. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign "quantities" to the ''[[chain (algebraic topology)|chains]]'' of homology theory.