 Universal coefficient theorem

The universal coefficient theorem relates homology or cohomology with different coefficient groups through tensor and Tor, or Hom and Ext, respectively. The universal coefficient theorem for homology is its tensor-Tor sequence; the universal coefficient theorem for cohomology is its Hom-Ext sequence.

The Universal Coefficient Theorem is a fundamental result in algebraic topology, particularly in the context of homology and cohomology theories. It provides a way to relate the homology of a topological space to its homology with coefficients in an arbitrary abelian group.