# cohomology

Cohomology is a subject that involves calculating algebraic invariants of topological spaces that are
formally dual to homology. The invariants
obtained are in general more powerful than those given by homology and usually
have more algebraic structure. **Generalized cohomology theories**,
both for topological spaces and for purely algebraic structures, have been
developed that have some of the formal properties of cohomology but which
don't have the same geometric background.