Definition of "cohomology"

cohomology

noun
countable and uncountable, plural cohomologies
1. (mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.
  Quotations
  In section 1 we start off by recalling some fundamental results in cohomology of groups, in particular the Evens–Venkov result on finite generation of the cohomology ring (Theorem 2) and Quillen's landmark result which describes H*BG up to F-isomorphism (Theorem 5).
  2001, William Dwyer, Hans-Werner Henn, Homotopy Theoretic Methods in Group Cohomology, Springer Science & Business, page 55
2. (mathematics) A system of quotient groups associated to a topological space.