Cohomology(C,n):: CochainComplex, Int --> List
Cohomology(F,n):: CochainMap, Int --> GroupHomomorphism
Cohomology(K,n):: CubicalComplex, Int --> List
Cohomology(K,n):: PureCubicalComplex, Int --> List
Cohomology(K,n):: PurePermComplex, Int --> List
Cohomology(K,n):: RegCWComplex, Int --> List
Cohomology(K,n):: SimplicialComplex, Int --> List

Inputs a cochain complex C and integer n \ge 0 and returns the n-th cohomology group of C as a list of its abelian invariants.

Inputs a chain map F and integer n \ge 0. It returns the induced cohomology homomorphism H_n(F) as a homomorphism of finitely presented groups.

Inputs a cubical, or pure cubical, or pure permutahedral or regular CW or simplicial complex K together with an integer n \ge 0. It returns the n-th integral cohomology group of K as a list of its abelian invariants.