Chain Equivalence
Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and gamma:D_*->C_* such that phi degreesgamma is chain homotopic to the identity on D_* and gamma degreesphi is chain homotopic to the identity on C_*.
See also
Chain Complex. Chain Homomorphism, Chain Homotopy, Homotopy Equivalence, Snake LemmaThis entry contributed by Todd Rowland
Explore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Rowland, Todd. "Chain Equivalence." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ChainEquivalence.html