cohomology

co- +‎ homology

cohomology (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.
   • 2001, William Dwyer, Hans-Werner Henn, Homotopy Theoretic Methods in Group Cohomology, Springer Science & Business, →ISBN, page 55:

     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).

2. (mathematics) A system of quotient groups associated to a topological space.