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Chain Equivalence


Chain equivalence is an equivalence relation on chain complexes. Two chain complexes are chain equivalent if there are chain homomorphisms phi:C_*->D_* and gamma:D_*->C_* such that phi degreesgamma is chain homotopic to the identity map on D_* and gamma degreesphi is chain homotopic to the identity map on C_*.


See also

Chain Complex, Chain Homomorphism, Chain Homotopy, Homotopy Equivalence, Snake Lemma

Portions of this entry contributed by Todd Rowland

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Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Chain Equivalence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ChainEquivalence.html

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