Cohomology is an algebraic variant of homology, the result of a simple dualization in the definition. Not surprisingly, the cohomology groups H i (X) satisfy axioms much like the axioms for homology, except that induced homomorphisms go in the opposite direction as a result of the dualization. The basic distinction between homology and cohomology is thus that cohomology groups are contravariant functors while - Universal coefficient theorem - Document - PDFSEARCH.IO

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	Cohomology is an algebraic variant of homology, the result of a simple dualization in the definition. Not surprisingly, the cohomology groups H i (X) satisfy axioms much like the axioms for homology, except that induced homomorphisms go in the opposite direction as a result of the dualization. The basic distinction between homology and cohomology is thus that cohomology groups are contravariant functors while Add to Reading List Document Date: 2013-07-18 16:41:10 Open Document File Size: 1,20 MB Share Result on Facebook Company Ker / H 1 / Hom / H 0 / Cn / Coker / / Event M&A / / Facility building C / / IndustryTerm chain groups / cellular chains / cup products / cohomology groups / hypothetical product / natural product / homology groups / cup product / topological / cross product / chain / fixed abelian / direct product / actual solution / simplicial cohomology groups / abelian / dual / cohomology / homology / / Position left end / / SocialTag Algebra Algebraic topology Homology theory Cohomology Cohomology theories Homology Universal coefficient theorem Chain complex Sheaf Abstract algebra