Direct sum of complexes in chain complex

algebraic-topology homological-algebra

Solution 1:

If $C_\bullet$ and $D_\bullet$ are chain complexes with boundary maps $\partial_C$ and $\partial_D$ respectively, then their direct sum is defined to be the chain complex with $n$th term $C_n \oplus D_n$, and with boundary map $$ C_n \oplus D_n \xrightarrow{\partial_C \oplus \partial_D} C_{n-1} \oplus D_{n-1}. $$

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