Tate cohomology

Tate cohomology is a mathematical tool used in algebra to analyze how groups act on algebraic structures like modules. It combines two concepts: invariants (elements unchanged by the group) and coinvariants (elements related through the group's action). Tate cohomology captures information about both, providing a more complete picture of the symmetry and interactions within the structure. It's particularly useful for understanding cases where traditional cohomology or homology alone don't give enough insight, especially in contexts involving finite groups and their representations.