In mathematics, the homology or cohomology of an algebra may refer to
Banach algebra cohomology of a bimodule over a Banach algebra Cyclic homology of an associative algebra Group cohomology of a module over a group ring or a representation of a group Hochschild homology of a bimodule over an associative algebra Lie algebra cohomology of a module over a Lie algebra Supplemented algebra cohomology of a module over a supplemented associative algebra
See also Cohomology Ext functor Tor functor