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.
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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.