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I came across the following statement in a textbook I am reading, and I was wondering what is meant by the abelian group of homotopy classes of chain maps. Could you help me out?


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You should say what textbook it is so an answer at the appropriate level can be given. Are you just learning about singular homology or chain complexes in general? – Henry T. Horton Mar 22 '13 at 22:27
I really just want to know what the abelian group of homotopy classes of chain maps looks like. Is it under addition? – Susan Mar 22 '13 at 22:42
Yes, chains have an additive structure, so $f + g$ makes sense, and on the level of homotopy classes we have $[f] + [g] = [f + g]$. – Henry T. Horton Mar 22 '13 at 22:47

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