Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain
maps 
and 
such that 
is chain homotopic to the identity on 
and 
is chain homotopic
to the identity on 
.
Chain Equivalence
See also
Chain Complex. Chain Homomorphism, Chain Homotopy, Homotopy Equivalence, Snake LemmaThis entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd. "Chain Equivalence." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ChainEquivalence.html