HomR (D, A) -+ HomR (D, B)-'.
The definition H(C)= Kerd/Imd can be written asH(C) -Coker (d': C-.. Kerd), where d' is induced byd. C). 2. For a family C1, tET, of differential groups, define the direct sum Z Cr and the direct product II C, and prove that H(E Cd agZ H(Cs). H(II C dc-- II H(Cr). 2. Complexes In the usual differential groups C of § 1 we can assign integral dimensions to certain elements of C. The set C. of all elements of dimension n is a group, C is the direct sum of the It and is more effective to work directly with this collection of groups.
Homology (Classics in Mathematics) by Saunders Mac Lane