Morphisms in the category $\text{Comp}$ are abelian groups? I'm reading Rotman's Introduction to Algebraic Topology and he states that the set of morphisms between two chain complexes in the category $\text{Comp}$ (defined in the box below) is in fact an abelian group.

$(S_*, \partial) \in \text{Obj Comp}$, where $(S_*, \partial)$ means
  chain complex.
Hom$(S_*', S_*) = \{ \text{Set of all chain maps between $S_*'$ and
 $S_*$}\}$
Composition is defined as: $\{f_n\} \circ \{g_n \} = \{f_n \circ
 g_n\}$, for chain maps $f=\{f_n\}$, and $g=\{g_n\}$.

He states that if $f=\{f_n\}$ and $g=\{g_n\} \in $ Hom $(S_*', S_*)$, then , $f + g \in$ Hom$(S_*', S_*)$.  I'm trying to prove to myself that this is a group, but what does this operation represent?  What is $\{f_n\} + \{g_n\}$?

$\{f_n\} + \{g_n\}$ is the family of morphism of abelian groups $S'_n \to S_n, x \mapsto f_n(x) + g_n(x)$. 
