Chain equivalence is an equivalence relation on chain complexes. Two chain
complexes are chain equivalent if there are chain
homomorphisms 
and 
such that 
is chain homotopic
to the identity map on 
and 
is chain homotopic
to the identity map on 
.
Chain Equivalence
See also
Chain Complex, Chain Homomorphism, Chain Homotopy, Homotopy Equivalence, Snake LemmaPortions 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